Four cities are World Heritage Sites: Lübeck, Stralsund, Wismar and Greifswald. Lübeck ist the biggest and most important one, but Stralsund and Wismar are better preserved. I like Stralsund the most. You should also visit the former capital of the duchy of Mecklenburg, Schwerin. The city offers a beautiful old town surrounded by lakes, but the highlight is the 19th century castle. A few miles to the south is Ludwigslust, which was the capital for 30 years. It's basically just a castle with a big park and some government buildings, but pretty nice. If you interested in architecture see the castle of Güstrow, the most important Renaissance castle of Northern Germany. I would skip Rostock, which was mostly destroyed in WW2. The best part of it is Warnemünde, a seaside resort. Close to Warnemünde is Heiligendamm, the first seaside resort on the continent. From there you can ride on a nostalgic steam train to Bad Doberan, where the minster is a must see. One of the most beautiful builings of the Brick Gothic.
The Baltic coast is the most popular summer destination of Germany, because of the sandy beaches and beautiful spa towns. The most popular areas are the Darss peninsula, Rügen and Usedom island. Usedom is basically a 30km long beach with beautiful 19th century resorts close to the Polish border, the so called Imperial Spas. On the northern end von Braun develoved the V2. Rügen is the most diverse and interesting island, with beautiful nature, many sights (the biggest Nazi building for instance) and good and beautiful resorts. On the western side of Rügen is Hidensee btw, a car-free island which was and is popular among the German elite. The Darss feels less touristic and more rural. Instead of posh 19th century spa architecture you find many fishermens houses with colorful doors there, and the Weststrand (western beach) is often billed as one of the 20 most beautiful beaches of the world.