There are three Hyatt Places in Deira, the older part of the city. The Al Wasl location is a very attractive new building with a full free breakfast. (You might have to be enrolled in World of Hyatt to get the breakfast.) The area is not where most tourist attractions are, and can experience traffic in the last mile to the hotel, but there are tons of taxis and there are two metro stops a few blocks away, plus a mid-level mall across the street. There are lots of local Indian and Arabic restaurants. Ditto for the Al Rigga location. These are both a longish, but doable, walk from the Deira waterfront, which is a must-see with the boats and souks. The Al Wasl location has a small but nice rooftop pool which is heated and offers decent views. Almost all hotels in Dubai have a pool anyway.

Another option might be Al Barsha/Mall of the Emirates. There is a new Hilton Garden Inn with a breakfast a bit less substantial. Also a handful of restaurants, plenty of taxis, and a Metro a few blocks away. This area is slightly farther from the Dubai Mall/fountain, which you will probably want to visit, but closer to the amusement parks and Jumeirah Beach.

There's another HGI in Al Mina, close to the beach and some pedestrian shopping areas. I am not as crazy about this location, but it's more suburban and more upscale than Deira.

Stay somewhere in Deira. Preferably close to Al Riga street. Right there you have metro stop, shopping mall and hundreds of restaurants. During my visits to Dubai I stay at HGI Muraqabat in Deira 30+ stays. During my first visit I've stayed at the private apartment, but it was over kill for 1 person. Had 2 bedrooms, 2 bathrooms, kitchen and living room.
HGI provides free shuttle to the metro (if you can't walk 2 blocks) and shopping mall (it runs on schedule). You can also buy in the lobby tickets to Khalifa tower. That way you will skip long lines in the mall.
This HGI is across the street from huge supermarket Al Kabayel, next to 3 banks with ATMs. It has a pool on the roof, restaurant and a bar downstairs and even hair salon.
In summer you can get rooms for as cheap as $40 a night, and in winter average price is around $110 per night. That's my go to hotel while I'm in Dubai.

Dubai—A city of dreams
 

Dubai—A city of dreams and the ideal world of the Middle East. Fantastically tall and magnificent structures rise overwhelmingly out of the desert sands and glimmer next to the shimmering blue Persian Gulf. Including the world's tallest structures; ATM's apportioning gold bars; biggest strip malls on the planet; cooled transport stops; most significant moving wellspring and so forth. With all the first class and world class things stuffed in one tiny emirate, Dubai has everything travellers searches for in their last most loved Fiesta. In any case, past every one of the sparkles and golds, there are some incense-wreathed vividly decorated mosques that keep it's social and customary eccentricities alive. It appears as though all the Arabian night characters and area has woken up.

If you're looking for the ideal combination of fewer crowds and pleasant weather, the best time for sightseeing in Dubai is between mid-November and early December, and again during the first half of March