You might want to play some rounds at Trelleborgs Golf Club, located 3 mi (4.8 km) from central Trelleborg. If Trelleborgs Golf Club doesn't quite scratch your golfing itch, Maglarps GK is also nearby.
You can spend an afternoon exploring the galleries in Trelleborgs Museum in Trelleborg. Stroll along the waterfront or visit the churches while you're in the area.