If you stay somewhere downtown that is near the light rail, that will give you access to the Museum District (MFAH, Contemporary Craft Center, Asia Society, Holocaust Museum, Museum of Natural Sciences), Hermann Park, Rice University (which is nice to walk around) and the Zoo. Keep in mind it would still take some walking to get to all these places from the light rail stations but by November it would be nice enough weather to walk around assuming it's not raining. Downtown would also put you near the ballet, theaters, symphony, opera. Houston has excellent performing arts if that is your taste.
Houston is also getting to be quite a foodie area. There's some stuff downtown, but you would need to taxi to a lot of the better-known places, many of which are west of downtown along Westheimer and nearby streets...but then again with a cab you can have as many cocktails as you like (Houston is also a good drinking city.)
Houston isn't really a tourist city...the amenities are for the residents and for those who are visiting for other reasons (the medical center etc) and it is assumed most people will have cars. But you can work around it.