House Park in Austin is the best skate park in the world. Right around the corner is No Comply, so if you feel like skating spots they'll help you out. There are a ton of spots in Austin. But really, House Park has pretty much everything you'd really want to skate anyways, except pool coping. If you want that, go down to Lockhart. It's a cool small town about 20 min south of Austin that has a tranny oriented park that can be pretty gnarly. If it's a weekend there will more than likely be a full old dude/shredder session going on.
Austin has really stepped up its BBQ game in the last couple years, so chow down on that while you're here. Micklethwait, La Barbecue, and Franklin are probably the best BBQ you will ever have. La Barbecue has free beer while you wait too, until the keg runs out. Franklin is really the best, but if it's a weekend, you really have to be there by 8am to secure your spot in line and guarantee you will actually get to eat before they sell out at 1pm. It isn't a bunch of yuppies waiting, that's how you know it's good. You can drink while you wait, so you can kill a morning doing that.
If you're a vegetarian, I can't help you. The Whole Foods flagship store is downtown, so there's that.
If it's hot out (there's really no telling in Texas until May, then it's just scorching all the time) you can go to Barton Springs, which is an amazing pool made from a natural spring. You can also rent canoes and go out on the lake that runs right along downtown.
If it's raining, go take a tour of the Capitol. Or do it regardless, it's awesome.
Not much in between Austin and Houston. In Houston is the new Spring skate park. It's the biggest in the country, which is honestly a little overwhelming, and helmets are required. Don't know much to do in Houston, but NASA is just outside and is pretty cool.
Hope that helps a bit with Austin at least.