The hill country is much more enjoyable in the warmer months... I think the biggest draw is the proximity to all the fresh water of the surrounding lakes/rivers/springs that you won't be able to enjoy in November. I'd stay in houston for a couple days then austin for a couple. Do yourself a favor and try to head down to gruene, tx about an hr south of austin and catch a show in the most iconic dancehall around.
Houston is not much of a city to see, unless you grew up here or work here I don't see why you would want to visit. For one you have to have a car to get around. There aren't really any "attractions." Houstonians don't mind tearing anything town for a strip mall or parking lot. I guess NASA might be something unique, but NASA is shell of itself. I think houston is trying to do better with bayou park renovation and things like discovery green, but houston doesn't really try to preserve things.
There's plenty to see, imo. But you have to like things like museums, symphonies, musicals, etc. The night life is improving with midtown getting crowded and the restaurants are great esp if you're willing to spend.
Food, food and more food. Lots of different types of restaurants. Great Indian/Pakistani restaurants, great Mexican restaurants, great BBQ, great steakhouses, great burgers, great Vietnamese food, lots of sushi places, lots of great coffee places, lots of great food trucks and great chains only local to Houston/Texas such as Whataburger, Beck's Prime, Papas.
No it isn't Downtown is pretty nice. They extended the riverwalk so you can bike along it. Its like 7 or 8 miles. There are also markets and stuff and pretty good tres leches.
I wouldn't call it a dump if it's in comparison to Texas attractions. It's geared more toward tourists than Dallas and Houston are.
I'm not hating their basketball team, just don't like the city. It's a fugly city. And Barkley is right, that's no river it's a dirty creek.
Galveston is just a 30 minute drive from Houston. If you want to relax on the beach or ride in the ferry, you can go to Galveston. There are a lot of things to do in Houston depending on your personality. Really a lot of restaurants here.
I would never recommend Galveston to someone coming to visit the US. Especially someone coming from Australia, where they have nice beaches and easy access to get to Bali or even Thailand. Galveston is a factory of sadness in comparison
Austin if you want to party with hipsters and college kids. Eat good food. Catch some random live music. Want to hike or do something outdoors. Houston if you want to checkout museums, buy ****, eat the best food in Texas and have the means to travel around. San Antonio if you want to to be around families, relax, have some margaritas and sloth around. Seaworld + 6 Flags - again, families.
I mean, Houston is a nice city with fun stuff to do... but there is nothing particularly unique about Houston in terms of things tourists can't find elsewhere. But you can still have a fun couple days. Go to the Rockets game, go to the Galleria Mall, eat at some good restaurants, explore the city a bit, etc.