Meissen has a pretty old town. It is hard to name the most beautiful spots. Walk around, and explore. Strolling the lanes and the stairways on the hillside aimlessly is the best way to find romantic views.
From the train station you will reach market square first when crossing the Elbe on the big bridge. This lower part is rather flat, with houses of wealthy citizens. The streets around the square have many little shops, including some that sell woodcarvings, china and other regional souvenirs.