Schwedt an der Oder is now a National Park town, close to the banks of the Oder River, and the Polish border. Schwedt was an industrial town, and therefore doesn't have as many large pedestrian-only zones as some German towns, so if you hire a car in Schwedt then there is plenty to get around and see.
There has been a settlement on this site since the 6th century AD, and the area has a number of beautiful churches, and a tobacco museum. The old gasworks have been converted into a hot baths, and part of the old city wall still stands today.
Because of the city's industrial past, getting around by car is easy, and hiring a car in Schwedt will give you more sight-seeing options. There are some wonderful buildings in Schwedt itself, but just outside is the National Park, which has 60km of beautiful countryside.
There are also the ruins of an ancient castle, built in the early 14th century, built to protect the border between Brandenburg and Pomerania. The town also has several Baroque sculptures, and a Jewish baths. The different parts of the town are quite spread out, so car hire in Schwedt is a good idea if you want to make the most of it.