The most popular attraction in San Antonio next to the Alamo is the River Walk or as they say in Spanish, Paseo Del Rio.
In order to get your bearings the first thing I suggest is to take a river cruise. The narrated tour is a great way to find out where everything is located.
There are many shops, restaurants and hotels located along the river. There is also a rather large size mall, which includes an IMAX theater.
The early morning is the best time to walk along the river while at night the river gets rather crowded and noisy.