There's plenty to do in Austin that isn't a tourist trap, and meets your nature stuff/sightseeing goals.

Round Rock is mostly a suburb of Austin now, with a small "old town" area and mostly just suburbia surrounding it. Expect a lot of chain stores and strip malls, along with the massive Dell HQ.

Matt already hit on the Alamo Drafthouse. I highly recommend this too, even if it's not in the nature/sightseeing category. Austin proper has 4 locations, and you can either go to see a normal movie or a special event. Get there 45 minute early, they run a pre show reel instead of ads, and getting there early will let you browse the menu without missing the movie. They normally ask, but if not, make sure to let the wait staff know it's your first time so they explain how everything works. Don't worry, no embarrassing situation here by telling them this. One of the regular special events I'll point out is the Master Pancake Theater. Think of this as a live version of Mystery Science Theater 3000, though a little more crass at times. http://drafthouse.com has all their schedules. Lake Creek and The Village are the ones on the north side of Austin and closer to Round Rock. Lake Creek would be easy to get to if you take the 45 toll road. Village, you will want to get to Mopac (Loop 1), and that can also be accessed off the 45 toll road. Ritz is downtown, and South Lamar is south of downtown.

Sightseeing on the nature area, Barton Creek and Zilker Gardens should be on your list. It's near downtown on the south side, and the parks offers a lot of areas to walk around, along with some kayak rental places at Zilker if you want to go sit on the lake. Even with the drought, the lakes have plenty of water in them still for boating, due to the dams. The area suffers from both drought and flood conditions, so a series of dams were built back in the early to mid 1900s to bring it more under control. You will see LCRA all over the place, that stands for Lower Colorado River Authority. The Mansfield dam near Austin has a public parking area both near the top of the dam (right turn off Loop 620 after you pass the dam, if headed southbound), and at the bottom (before you pass the dam, left turn off 620).

Also, if you enjoy driving through scenic areas, I'd recommend a complete trip down Loop 360 in Austin, to see the mix of commercial buildings and protected land. It's a nice balance, and is an amazing place to work. If computer games interest you at all, you can look for the old Origin building. It's a large white office complex one stop light right before the bridge over the lake. If you are driving northbound on 360, it's easy to see before even crossing the bridge. Southbound, you won't see it unless you turn off to do so, or unless you look in your rear view mirror after crossing the bridge.

One restaurant I'd recommend more for the scenery would be Ski Shores Cafe (2905 Pearce Road
Austin, TX 78730-4310). This is in the 360 area, and driving there will take you on some pretty fun residential roads. Richard Gariott's castle is nearby, along with some other amazing properties.

If you have time to escape town all together, I'd recommend a drive out into the hill country. For example, the route from Austin to Marble Falls along FM 1431 is pretty nice. You can even take a few detours to go look at Lake Travis along the way.

I've got plenty more to post, but this will start you off on things to look up to see if it interests you.