The greatest concentration of homes that match your criteria (3br, 2200-2500sqft, $325-400k) is in Lakeway. There are 9 homes here that meet your needs. Lakeway is basically a suburb of Austin sitting on Lake Travis with easy access to the Beaches, boat ramps, and Waterside entertainment. Lakeway is about a 20-25 minute drive to downtown. Lakeway homes in your price range provide some of the most breathtaking views of the Lake and surrounding Hill Country.
There are also 5 homes in Central Austin that fall into your range. Downtown is literally 5 minutes away. You have easy access to major highways, Austin culture, and local events. Central Austinites are often a different breed in that the Austin neighborhoods (Tarrytown, Clarksvile, Barton Hills) each have their own identity as close nit communities. Most of these people whom I've encountered think the rest of us are crazy for living more than 5 minutes from all the action.
Yet 5 more properties are in Southwest Austin. The best way to describe this zone is urban suburban. You will still find many trends and attitudes of the downtown scene, but things are a little more relaxed and you have a bit more space to stretch your legs. Homes hold their value here due to the proximity to town and quality construction of the community.
Finally, there are 3 homes in Dripping Springs you might like. Dripping Springs is a rural community where there is an interesting weave of high end homes and abundant farmland passed down through the generations. While it continues to grow, most of the folks I know in 'Drip' seem to like things just the way they are.
Some of the other areas mentioned below (Round Rock, Northwest Hills, Steiner Ranch, etc.) are also great choices. What I have found though is that the homes here are typically larger than what you specified for the price. Round Rock is dealing with sagging home values due to increased inventory. You might find some great deals on houses here, but there is no telling when their value will sustain. Northwest Hills is a wonderful place with captivating mountaintop views, but these homes are typically priced well into the $400's and above. Steiner Ranch homes hold value fairly well, but again, they are quite large.
If you are looking for a new home, then Leander offers the best value for your buck right now. Crystal Falls is an incredible community where you can get a top notch new home in a master-planned community for a relative value.
Hope this helps. You may contact me if you are interested in receiving these highly targeted listings or new home suggestions.
Good luck and remember..."It's ok that you aren't from Texas. Just get here as fast as you can.:)"