"sleep around" and "get around" certainly exist here, though they're fairly recent -- as in since the 1950s? -- presumably american imports originally, though i doubt they'd be tagged as such now: the american usage has basically arrived to stay in lots of forms

eric partridge, writing in usage and abusage (1st edn late 40s), says that "about town"/"about Christmas" is correct, and "around town"/"around Christmas"/"round town"/"round Christmas" are incorrect (unless you actually mean walking round the town perimeter) -- so presumably would have preferred the beach boys to sing "i get about" rather than "i get around" -- but all the arounds/rounds are commonly used these days

even now i would say that "i walked all around town" involves more expansive journeys than "i walked all about town", though the latter now feels a tiny bit dated perhaps -- at least in middle class or london english