In BrE we'd normally say 'I like to get about' if the meaning is related to moving from place to place. 'I like to get around' carries a slight suggestion that the individual has lots of sexual partners. We wouldn't use 'go around' on its own like that, it would almost always be follwed by an -ing phrase - 'I like to go around checking the doors are locked', or 'I like to go around visiting my friends'.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.