Since it is for short-term, you may be having a difficulty finding one which suits your preference and budget.
Individual owners whose property may be available through HAR are usually reluctant to rent for a short-tem contract, in my opinion, because they have to pay certain amount to the Realtor.
My friend who is very familiar with Houston areas told me that the area you had mentioned, between westpark/westheimer and Gessner/beltway 8 was not recommended. I personally drive that area often and I guess I know why my friend told me so.
I had a friend who lived in Yorktown Apartments, if my memory is correst. It was a pretty big and nice community, close to Galleria.
I guess this is available through apartments.com. and short-term lease is also available, so you may want to take a look.
If medical center is within your criteria, Archstone and Brompton have short-term lease, I guess. Either of them is also available through Apartments.com.
Actually, the traffic heading north from med center is not as bas as that from north to med center.
Or you may want to consider using Apartment Locator service. It is free and maybe easy.
I hope you can find a good one! Good luck!!