You can send them shopping (they'll come back with new clothes), to dance classes, to local attractions, to gambling spots, to take on some part-time work, and more. Once your Sims have visited the DMV for a license or bus pass, you can send them exploring just by clicking on them, which brings up a radial wheel of options.
This mod from KawaiiStacie adds a bunch of rabbit hole actions-activities your Sims can do on their own without you following-that activate buffs or improve your Sims' relationships with those closest to them. (Image credit: Electronic Arts, Maxis / Modded by KawaiiStacie)
