A 1bdrm apartment for a year will likely run you $1200-$1600/month in the 15 years old or newer type communities. Month to month, furnished with utilities paid for, etc can run as high as $3,500/month.
That "Galleria" area is the heart of the city and very popular with singles and those new to town. You can find less expensive apartments and privately owned condos a few miles out (west). Private properties will likely only lease for a year at a minimum. Apartment communities have 6 month and in some cases, 3 month options.
I can provide you a list that meet your parameters and a way to view it on-line, see photos of the community, floor plans, etc. Let us know if we can help you. No charge for this service!
Bernstein Realty, Inc.