Rostock

It's very easy. The train station is directly on the pier, and a day tickets costs 3,30€. Have a look here: Timetables, tickets, fares

But you could do much more on your own than just Rostock. The city is quite nice, but was partly destroyed in WW2. There are some more interesting sights than Rostock which you can easily do on your own. You could, for instance, see

• Bad Doberan, Heiligendamm and Kühlungsborn. Bad Doberan was the former summer residence of the Mecklenburg dukes. The highlight of this pleasant town is the Doberan Minster, one of the most beautiful medieval churches of the Baltic coast. From Bad Doberan you could take the Molli, a nostalgic steam train, to Heiligendamm, the oldest seaside spa on the continent, and to Kühlungsborn, a nice spa town. A day ticket, which includes the Molli, costs 12,70€ or 38€ for a group.
• Wismar and Schwerin. These are two beautiful old towns. Wismar is a World Heritage Site and a almost completely preserved Hanseatic town, "only" one church was lost in WW2. Schwerin is the former capital of the duchy of Mecklenburg. The beautiful, preserved old town is surrounded by lakes, and the 19th century fairytale castle is one of Germanys highlights. Use a "Länderticket" for this tour, which costs less than 30€ for two people. The Länderticket however is valid only after 9am, if you start earlier you need to buy a regular ticket for the first leg.
• Stralsund. Stralsund is the best preserved Hanseatic town in Germany, and a World Heritage Site just like Wismar. The old town is very nice, and the museums are quite interesting. The German Oceanographic Museum is in a old monastery, the Ozeaneum in a impressive new building at the harbour (where you can see the Gorch Fock), and the town museum is one of those old, charming museums you only find in small towns.

Martin, thank you very much. Your answer is very helpful.

Martin's advice looks pretty sound.