If seeing the sights is on your list of things to do, head to Häljesta Petroglyphs— just one of the landmarks located 4.7 mi (7.5 km) from central Köping.
Strömsholm Palace is just one of the landmarks located 0.6 mi (0.9 km) from central Strömsholm, so you might want to stop by for a few pics during your trip.
You might want to play some rounds at Skerike's Golf Course, located 3.5 mi (5.7 km) from central Vasteras. If Skerike's Golf Course doesn't quite scratch your golfing itch, Vasteras Golf Club is also nearby.