I live outside the loop (610) on the west side just off of Woodway. You can take Woodway/Memorial straight into downtown and it takes maybe 15-20 minutes in the mornings. It's a nice area of town, but you can find a pretty wide range of apartment prices.
What range are you looking for, any special amenities, pets, etc.?
I may be a little late to jump in, but perhaps you are still monitoring this thread.
You should ask some questions of yourself. What kind of surroundings do you like? Are you and urban rat or a country boy? Or you with or without spouse and children? If you have children, you may want to seek the more open spaces of the suburbs where it may also be easier to find better schools. This usually means living OTL (outside loop 610) which for me always divided the real city dwellers from the others.
I would definitely be on the urban side if I still lived in Houston and worked downtown. I would live deep downtown. A lot of loft space has become available for both rent and purchase over the last 5 or so years. Just south of the heart of downtown is what is becomming known as midtown now that it is getting gentrified. There is lot of new apartment space going up in that area. This happens to be the area where the Continental Club, an Austin import you may be familier with, opened its Houston doors a while back.
For something rather different take a look at the Heights just north and west of downtown. Here you're talking old fashioned wood frame houses, remodeled old complexes, and garage apartments. Some of the old houses are quite large and attractive. This area is very popular and not cheap if you want to buy, but you should be able to find reasonably priced rental space.
There is always the Montrose. Older, funkier, gayer, whatever.
The med center and West U are close together and both are close to Rice Unviversity if that would hold any interest for you. Most of the surroundings of Rice are fairly pleasant. West U is nice, but very expensive, at least to buy in the area.
I have lived in both Austin and Houston. I actually prefer Houston strangely enough. I liked to live close and avoid the commute.