UH is in Third Ward, not Downtown. There's a separate branch of UH (UHDowntown)--that's in downtown. Third Ward is one of the hoods, but also has nicehouses and is in close proximity to downtown and the Museum/Rice/Medical Center areas.
You do NOT want hood bars/clubs? Depending on your style of dress (that is, dressing up or being very casual), there are TONS of options. Downtown is now knownmore for all the hood clubs on Main Street. Maybe not "hood" in the sense of getting shot, but hood in the sense of not upscale. Washington (astreet), Midtown, and Rice Village are your best options for non-hood, upper-scale, options--everything from shortsshirt to more dressy type places.
For shopping, the malls/areas are pretty much decided by your budget. If you like the best stuff, go to The Galleria. Uptown, Highland Village, Rice Village,Memorial City Mall are all pretty good, too, but all the big designers are in The Galleria--Montrose area has cool stuff if you're into hipster-likeclothing. If you're looking for hood stuff, go to Sharpstown or Greenspoint.
If you're not into the "hood" culture, you'll have virtually no reason to ever go to the Northside of the city unless you're shopping forcheap furniture.
Feel free to PM me for more info. I've lived here for 22 of my 23 years, and know a thing or two about this place.