Burnet is convenient to the Higland Lakes: Lake Buchanan, Lake Marble Falls, Inks Lake, and Lake LBJ. This chain of lakes has opportunities for swimming, boating, kayaking (rentals in Marble Falls and Buchanan Dam), water activities, and fishing. Some like to hire a local guide to take them out for fishing - be sure to ask your guide about fishing license requirements BEFORE you head out. Other people are happy with just fishing from the shore. If you fish in a Texas State Park, such as Inks Lake State Park, you do not have to have a fishing license - but be sure to obey all other regulations! .
Several excellent golf courses are near Burnet. Delaware Springs is just south of town, and there are also courses near Marble Falls, Kingsland, Llano, and Horseshoe Bay.
Burnet's City Parks have disc (frisbee) golf courses and a skate park. For other activities, you may want to visit the YMCA of the Highland Lakes on Hwy 281.
If you're up for hiking, biking, or even scuba diving, Reveille Peak Ranch off of Hwy 29 offers trails and race events. (Of course hiking and biking are available at the state parks on Park Rd 4.) If 4-wheeling, dirt biking, or range shooting is more your style, you can visit Hidden Falls Adventure Park in nearby Marble Falls.