One of the great things about Georgetown is the local hike and bike trail system. The City maintains a several trails that essentially begin at San Gabriel Park. From here you can take the South fork trail to the downtown area and visit the square for shopping or dining or continue to follow the trail to Blue Hole swimming area.
For those a bit more energetic, The North fork of the San Gabriel river trail will take from the San Gabriel park all the way to the Dam at Lake Georgetown. From there you can visit several LCRA parks or connect to the Goodwater trail, a 26 mile trail around the lake.
There are several trail heads and multiple access points to the Goodwater Trail system allowing for short day hikes or multi day trips. The most common starting point for a hike along Lake Georgetown is at Cedar Breaks Park, at the southeastern corner of the lake. Here the trail starts off on a well maintained surface of crushed stone, but within a quarter mile turns rocky and rough as it approaches the lake shore. Some of the best views of the lake occur near mile marker 1 on the trail and thereafter. This past weekend I hiked to Crockett Gardens, about 2.5 miles in. There is a nice oasis with a stream, lots of shade and just a very pleasant area to stop for lunch or take a break.
For more information about Georgetown and the trail system visit: http://www.sedlorproperties.com/102/206