I dont know what kind of shopping you are looking for. Just the same old stores at the mall?
Downtown - RW area, has some tourist shopping areas, and the malls with the larger chain stores are out north. If you are seeing the Alamo, Zoo, El Marcado, then RW area is best. If you are seeing Fiesta Texas and Seaworld, northside is best.
RW area, try the Holiday Inn RW or the Crowne Plaza, both are fairly reasonable. For the Northside, there are a number of hotels around the airport, a handful around Fiesta Texas and some more out by Seaworld.