renting a car vs train from warnemunde

This is the most rural region of Germany, but at the same time the most pupular summer destination of Germany. Not just because of the beaches but also because the Baltic coast offers everything from medieval towns, Gothic cathedrals and 19th century seaside resorts to Nazi relicts.
Here is a list what you could see:

Hanseatic towns
Lübeck, Wismar, Stralsund and Greifswald are medieval towns, with mostly preserved old towns, which were members of the Hanseatic League. Lübeck, the biggest of them, was the head of the league, Stralsund is the one I like the most. All four are World Heritage Sites.

Historic towns
Schwerin - was the capital of the duchy. The cute old town, surrounded by lakes, is a mix of 19th century government buildings and older half-timbered houses. The highlight however is the castle of the dukes, a 19th century fairytale castle just like Neuschwanstein.
Güstrow - is a typical provincial town with a preserved centre, a nice Gothic cathedral and the most important Renaissance castle of Northern Germany
Ludwigslust - was a summer residence of the dukes. It's a cute little village with a castle and a large English landscape park.

Churches
Bad Doberan - offers one of the most important churches of the Brick Gothic. The minster is completely preserved and just 15km to the west of Warnemünde. Bad Doberan itself was a summer residence of the dukes, and from there you can take a steam train to Germanys first seaside resort.

Nazi relicts
Prora on Rügen island is a 4km long concrete block, built as a resort on a very nice beach. Peenemünde on Usedom island is the place where von Braun developed the V2 rocket.

Seaside Resorts
They are the most distinctive feature of the German Baltic coast: posh 19th century seaside resort with their typical resort architecture. Most of the best resorts are to the east of Warnemünde, especially on Rügen (Sellin, Binz) and Usedom island (the three Imperial Spas Bansin, Heringsdorf and Ahlbeck).
BTW: Warnemünde is a nice resort too, with many old captains houses.

Nature
The most picturesque part of the region are the islands and peninsulas to the east of Warnemünde: Rügen is the most diverse, the Darss peninsula the most unspoilt with many old fishermens houses, and Usedom offers a 40km long beach.

What you can do:
You basically travel either to the west or to the east. If you travel to the west you can see Lübeck, Wismar, Schwerin, Ludwigslust, Bad Doberan and Güstrow. The most popular tour, also offered by local tour companies, is the combination Wismar, Schwerin and Warnemünde, which is simething like a Best Of the Baltic coast: Hanseatic town, fairytale castle, seaside resort. This can be done by train too, which is very cheap... less than 30€ for two. A car makes sense if you want to squeeze in the minster of Bad Doberan for example.
If you want to see the eastern part of the region a car makes sense. In this case you could see Stralsund, my favorite Hanseatic town, and Rügen with Binz, the poshest and most beautiful resort of the island, and Prora. Or Stralsund and the Darss peninsula. If you want to see Peenemünde on Usedom island you definitely need a car. Here a combination with Greifswald OR the three Imperial Spas Bansin, Ahlbeck and Heringsdorf is possible, but I don't think you can see all three on a single day.

If you don't want to do it on your own, Friends of Dave gets rave reviews on Tripadvisor:
https://www.tripadvisor.com/Attraction_Review-g187364-d1647222-Reviews-Friends_of_Dave_Tours-Warnemunde_Rostock_Mecklenburg_West_Pomerania.html

PS: if you travel by car don't drive to Rügen or Usedom on a Saturday! Traffic jams are pretty common on this day.

Thank You Martin, This is very helpful, our trip is in late august, so we will have time to plan this thanks to you.