I like Trip Advisor as people give pretty honest reviews, and it helps me choose a hotel when we travel. But, even better, use this site to find a place to stay in Dubai: www.airbnb.com . People all over the world post their apartments there at this site, and I find that preferable to a hotel as you have a kitchen! Usually, it is also a lot cheaper than renting at a hotel. So, I would try Air BnB before resorting to a hotel.
And, one thing to keep in mind: Dubai is HUGE!!!! I am not kidding. It takes over an hour to get from one end to the other, and that is without traffic. It is also very easy to get lost. So, I suggest 1) using taxis, don't drive, and 2) finding a place that is a bit central, and hopefully on a street where it isn’t too hard to get a taxi.
Interesting things to do:
Go to the beach!!! The beaches are lovely in the winter, with weather in the 70s/80s. Winter is the perfect time to hit the beaches, up until May. In June it starts to get a bit too hot, in July don’t go to the beach! :It is too suffocatingly hot then. And usually only foreigners go (no Emiratis), so you wear your normal bathing suit and not worry about offending the local cultures.
Visit the old town Dubai - walk around it, and check out the Souq. Do be prepared for the merchants to hound you to buy things. To that point, that is actually a reason to go when it is busy, they will hound you less when there are more people around. My husband and I went early in the morning, and were one of the few people there, and then everyone hounded us non-stop, as there was nobody else around. It did get a little aggravating.
There is the Gold Souq (market), and then there is the Spice Souq (Market) too, and several other types of Souqs, all within short walks of each other.
You can take the boat cruise on the canal too, on the traditional wooden boat of the fisherman, called a Dhow:
And, if you can, go to the Dubai Mall - not to shop so much as to just see it. It is HUGE - with all these sculptures, a ‘fish’ tunnel, a huge wall-waterfall, and other crazy stuff only those in the UAE with more money then they know what to do with would make!
The Dubai Mall is also right next to the Burj Khalifa (tallest building in the world), so you have to go up that. But, you have to buy your tickets for that online in advance… you cannot just walk up and go up it.
And, have lunch at the Burj Al Arab (it is near that crazy ‘palm leaf’ island they have made there):
As for dress codes:
No, you don't have to cover your hair! I am a women, and I never felt I had to change how I dressed either. But, then, I never dress inappropriately. I am no prude, but my wardrobe also never included cleavage-showing tops and Daisy-duke shorts and mini skirts. As long as you have respect, and cover your shoulders, skirts to your knees, no tank tops, then you are fine and can certainly wear the usual stuff you would wear on any US or European street.