If you are looking for a single place to stay Hamburg is indeed your best option, simply because it's the biggest city and offers the most for 3+ days. Lübeck comes next in terms of size and sights, but the city is too small for 3+ days, so plan one or two day trips.
FYI: Lübeck is one of four Word Heritage Sites (WHS) along the German Baltic coast. The others are Wismar, Stralsund and Greifswald. All are WHS for the same reason: they were part of the Hanseatic League and offer historic, medieval looking old towns. Lübeck, which was the head of the Hanseatic League, has the biggest old town, but also the one with the biggest blunders. since it was heavily destroyed in WW2. Wismar misses a church (also WW2), and Greifswald a old town quarter (Commies). Stralsund is probably the best preserved of the four.
Schwerin, the capital of the region and of the former duchy, is equally ineresting. While the previously mentioned towns look quite medieval, Schwerin is a a city of the 18th and 19th century, with many big government buildings of the era. The most famous one is the fairytale castle.
BTW: the area, the Baltic coast between Lübeck and the Polish border, is Germanys most popular summer destination. Not just because of the many historic towns, but also because of the great beaches, posh 19th century resorts, and natural beauty. It's a great place to spend a few days.