Sims will also randomly explore if you don't intervene, which is neat. Their skills and motives will change based on the activity you choose, and you can tell your Sim to 'Explore With' another character if you want to improve relations.
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)