The UAE is a lovely and unique place to spend a few days. I was not at first excited about Dubai since I expected it to be an artificial play land like Vegas and came primarily to visit a friend but once there I changed my mind entirely.
Dubai is the only place in the world which is new and shiny on such a spectacular scale and everyone should experience it for themselves.
Below is the total brain dump of all we would recommend you do and see when you come to visit. Will try to add some pics once we sort through them.
The beach
When in Dubai you should spend at least one a day on the beach. You can get a room at one of the many gulf-side resorts but they will be pricey. The great thing about Dubai is that almost every hotel lets you spend time on their loungers/by their beach/pool for a fee and this way you can sample multiple beaches and see many hotels without paying extra on days you don’t use the facilities.
The beach club place I loved the most was Nassimi Beach near the Atlantis hotel on the Palm. It has a lovely all white Ibiza feel, the food is fantastic and the DJ was great. I have also heard good things about Riva beach club. Do some research on the matter to find the latest and greatest when you go.
This leads me to one thing I noted: there are plenty of affordable hotel options in Dubai so you shouldn’t think of it as $1000/night place (though there are plenty of those). They won’t be beachside, or with spectacular views but since you will spend little time there and since you have to pay to get in most place, it won’t really matter. Don’t fret too much time about location because you have to take a car everywhere in Dubai anyway and since most places are new, whatever you get will likely be nice and spacious.
On the subject of budget options,
Jumeirah 1 beach is free, clean and pretty and has towels, loungers and umbrellas for rent at reasonable prices. We got there late towards the evening but I suspect that during the day there are plenty of food vendors around as well. It’s a great way to spend a beach day on the cheap.
http://m.departures-international.com/nc/sections/post/top-five-dubai-beach-bars.html
Burj Khalifa
I absolutely fell in love with this beautiful elegant enormous building, also known as the Burj Dubai. You can’t just stroll in to check it out though. To get inside you need to either have a booking to get to the observation deck or have reservations at the Armani hotel or one of the restaurants. Or, of course be a resident but that’s a little harder:) we decided that since we’re paying goos money we might as well get fed and booked afternoon tea and the At.mosphere restaurant on the 122nd floor. The food was ok and the views spectacular. If you make the same choice, ask for a table by the glass and with a view of the gulf where you can see “The World.”
You can and should also admire the Burj Dubai from afar. There is a beautiful fountain show every night and you can enjoy a great view of it and the magnificent tower from Zeta restaurant across the pond.
Burj Arab
Much as with the other Burj. you cant just walk into the sail. Go for Afternoon tea or lunch or see if from afar from the 360 bar that’s on the water.
Night life
Other great seaside spots to wind down are Jetty Lounge at the one and only royal mirage and Bliss lounge at Sheraton Jumeirah.
The Mall
You can easily spend a whole day the the Dubai mall. Other than every conceivable western chain clothing and shoe store (including a giant Bloomingdales) there are also dozens of restaurants, an ice skating rink, a huge aquarium (that you can dive in!) which at the time of our visit was home to over 80 sharks, a movie theater, sega republic indoor theme park and an Arabian indoor souk. The mall is huge and it’s easy to get lost so take your time, wander and enjoy.
The Marina
The marina is the large expat neighborhood with beautiful modern towers. Check out the Walk at JBR which has a Miami vibe. Great place for people watching and the insane diversity that is Dubai.
Caramel and Financial Center
Another great place to get to know the people of Dubai is Caramel in the International financial center. Here there are few tourists and most of the crowd are expats who work nearby. There are also quite a few Emirates who come here for dinner and a night out. We saw a table of ladies in abayas, an Emirati husband and wife out for the night and an Emirati couple out on a date mingling with people from Uk, Australia, the states, Philippines, Shri Lanka and India. It’s a great feel and a contrast to all the tourist packed places you have been and the food is great! After hours it’s also a good nightlife spot.
What we didn’t get to
Next time I would like to muster the strength for nightlife which is supposed to be great in Dubai. The djs we heard at lounges were awesome and I love the middle eastern sounds mixed in with more familiar beats. One place recommended to us was circue du suoir.
I would love to smoke a shisha. Like in Russia, many restaurants have shisha experts on staff and the smells wafting over to us were fantastic.
Also I would like to and suggest anyone who goes to sample middle eastern food. There are many French and Italian and American restaurants that cater to the expat crowd to its easy to ignore the fact that you are in the Middle East but Dubai is a great place to sample this cuisine.
Finally, I would like to do an Airplane or helicopter flight over Dubai and Abu Dhabi. It’s a city build on a large scale sandwiched between the desert and the water and it needs to be seen from above. These flyovers are pricey so plan in advance.
ABU DHABI
Abu Dhabi, the capital of the emirates and Dubai’s close neighbor makes for a great day trip. There are public busses that can take you there for a reasonable price (men and women sit separate on public busses fyi) or you can pay for a private transfer. Anything and everything in this part of the world has a regular and a luxe option 
You can spend the early part of the day on Yas Island: at the Yas water park (better than the ones in Dubai by all accounts) or Ferrari world. I didn’t get a chance to visit since we fell in love with the mosque (see below) but my taller half was there a few years back for the formula 1 and says its worth the trip.
Tea at Emirates Palace is lovely way to take a break from sightseeing. They serve the Same tea as the one Chinese royal family drink in a great opulent hall with live piano music so u feel pampered.
If old school tea is not your style, the sleek Ethihad towers next door are a good place for lunch, dinner or a drink at the observation deck.
A visit to Sheikh Zayed Mosque is a must. I would come in the early or the late part of the day to avoid the high noon sun and ideally at sunset for the most beautiful views of this strikingly beautiful place. There are no words to describe it but google images will give you an idea.
Keep in mind that the mosque closes for the 5 daily prayers so look up the times online and keep them in mind.
Loose clothing that cover down to wrists and ankles and a headscarf are required for women and no shorts for men. If you forget, don’t fret: you can borrow an abaya or a kaftan for free and feel like a real Emirati for an hour
The mosque was built for all to visit and see and the amount of design and work that went into it is stupendous. There are free tours a few times a day so check the times before you start.
The Island
Saadiyat Island is a great place to take a break around noon or for the stop before you head back. The Louvre Abu Dhabi museum is building its own collection and select parts are now on display on the Island. They are curated in a very original way. In a few years there will likely be buildings sprouting up and a larger collection to see.
The DESERT
If you come to the UAE you have to visit the desert! There are dozens of companies offering desert excursions and you should do some research to see what best suits your fancy. We wanted to ride around on dune buggies so we booked with Dream Explorer who took us on an awesome tour around the beautiful white-red dunes.
Two things I would love to do in the desert next time are 1. sunrise air balloon flight over the desert and 2. Stargazing tour. There are currently two major companies that do air balloon flights but more are likely to crop up as both of these were booked up.
As per the stargazing, Dubai astronomy site is a good resource and there are a few companies that so night safaris and overnight camps in the desert. Links to both below.
http://www.dubaiastronomy.com/
http://www.getyourguide.com/dubai-l173/heritage-night-safari-stargazing-t32135/
The Creek and the Souks
If you’ve ever spent time in Asia or the Middle East you will find the famous Gold and Spice souks underwhelming. There are shiny things at the Gold souk and nice smelling spices and wood at the Spice souk but much of the old character is gone and most of it is now just Grand Plastic and Crap Souk so if you’re short on time I would skip it.
Global Village and expos
A much better way to spend that time is to pay a visit to dubai village which has pavilions for various countries, many of them from the middle easy, where you can buy souvenirs and curiosities and learn more about the region at the same time. It’s only open during high season so check the opening and closing dates.
Also once you set a time for your trip, do some research on what expos are going on while you’re there. Dubai hotels are huge and numerous and there is always some kind of convention on and some are very interesting.
Longer Trip
There is much to see in the other emirates, in Qatar and nearby neighbor Oman if you have more time in the region.