Travemünde. Lübeck's own Baltic seaside resort, 20 minutes by S-Bahn. Long sandy beach, old wicker beach chairs, the four-masted Passat barque moored in the harbour, and ferry traffic to Scandinavia. The lighthouse, beach promenade, and the Maritime Quarter make a half-day easy.
Hamburg. 45 minutes by direct train — the obvious large city to pair with Lübeck if you have a few days.
Wismar. A smaller Hanseatic sister on the Baltic, also UNESCO-listed, an hour east by car (no direct train). Quieter, less touristed, with the great market square and St Nikolai church.
Ratzeburg. South of Lübeck on a lake, with a Romanesque cathedral and the home of the sculptor Ernst Barlach. A pleasant 40 minutes by train or car.