The Radisson Blu in Deira (Dubai Creek) is close to the airport and overlooks the Dubai Creek area. The Deira City Centre Mall is close by, as is the Souq. This is a great hotel -- 16 or so restaurants. I have stayed here a few times in a Royal Club Room, which was very nice.
I think the pool area is still closed for maintenance, however.
I stayed here over New Years. It was nice, quite elegant but also a bit dated. The rooms were small but comfortable. Location was great for old Dubai, walking distance to everything and being by the creek was nice.
If you want something more modern or something with a decent pool area for sunbathing, then I would go elsewhere, but for a nice first time Dubai experience, I'd recommend it. I would think hard about where you want to be based in Dubai though because the location may not appeal to everyone, and the city is very spread out.