Where do early 20s professionals live if they work downtown? (Travis St, JPMC Building)

I don't go out often, but I'd like nearby restaurants and casual bars. I also enjoy being outdoors and biking, so it would need to be a safe area (preferably near a park). I just graduated from UH, but this will be my first time living in Houston. In the past I've commuted from Katy on the metro, but I'd like to be closer to work on Travis Street (or close enough I can still catch a bus from my new place).