I recommend to go to Travemünde, which has a nice harbour-front walk with many historic buildings and nice views, shops and restaurants. And you can buy or eat fresh fish from the fishermen.

http://www.travemuende.de/tourismus/.../en/index.html

Travemünde can easyly be reached by bus, train (15 minutes) or even a boat tour from the center of Lübeck.