There are a lot of things to do in town. Most of them are on the riverwalk in downtown. The Alamo is a must-see for most; however, it is much smaller in person. The riverwalk also has a mall, shops, and restaurants.
Quick Tips: Stay on the river if at all possible. The nicest hotels are there, and you can find some great rates online.
Best Way To Get Around: You will need a car if traveling to the outer parts of town. If you travel to the riverwalk, you will have to pay for parking, but if staying at the hotels on the river, just park and walk the river. That way, you are not paying the parking garages twice.