There are several options to spend your time around Lübeck.
Sea-side towns for sun & beaches are:
Somewhat north of Travemünde is a cliff Brodtener Ufer that has a hiking way from Travemünde to Niendorf 1-1,5 hrs walk with good views on the Baltic coastline. Niendorf/Ostsee is somewhat more cosy and family oriented with its fishery port and a new renovated public swimming pool and a well-known bird zoo Vogelpark Niendorf, situated in a small nature resort.
The Baltic coast resorts in Mecklenburg Pommerania are about 1-2 hrs drive on the Autobahn A20 away and might be worth a day trip
For nature lovers a trip to the lakes south of Lübeck may be of interest as there are great opportunities for bird-watching eg the Ratzeburger See and the Schaalsee. Ratzeburg with its Ernst-Barlach and A.-Paul-Weber museums and Mölln are also worth a visit, especially as they are easily accessible by train. Near Ratzeburg is also one of the rare places to see the nearly extinct European bisonânot a very spectacular facility, just some buffaloes on a pasture, but if you're in the area and have never seen one you might want to look out for the "Wisentgehege".
If you're travelling on northwards to Kiel, consider a train stop in one of the three small towns of Eutin, Plön, and Preetz. Among other sites, each of them boasts a "SchloÃ" or former aristocratic mansion. The towns are situated in a lake district which is popular for rambling and canoeing in summer you can eg rent a canoe in Plön and go to Preetz by Schwentine River and through various lakes, then the canoe-centre people will get you and your canoe back to Plön by car.
And don't forget that it's just a mere 50 minutes by train to Hamburg they go each hour.
During the summer the Schleswig-Holstein music festival (http://www.shmf.de/) is one of the largest events in northern Germany. An abundance of concerts with world-famous artists and orchestras attracts many people every year.
