I've visited Harburg castle, but didn't stay there. I stayed instead in nearby Nördlingen, which I highly recommend. It's similar to Rothenburg, but far less touristy. It doesn't have a Christmas shop or a Crime & Punishment Museum, but those things aren't what I find interesting about an old, walled town. The surrounding wall is nearly intact - I think one section is missing - and the wall has a Wehrgang you can walk on. You can also climb the church tower in the center of town, where, on a clear day, you get a fantastic view of the surrounding land. Including overnight, I spend about 18-20 hours in Nördlingen.
The official Romantische Strasse website lists 25 stops between but not including the end points, Füssen and Würzburg. When I did the Road in 2007, I identified 10 of these places that I wanted to see. I spent most of five days, on the Road, including extended overnight stays in four towns, Landsberg, Nördlingen, Feuchtwangen, and Weikersheim. I started at Wieskirche, because I had already been in Füssen, and I only went past Rothenburg, where I had been twice previously.
I don't recommend Wieskirche, because it is somewhat out of the way and nothing unique. Later in the trip, I visited Andechs Monastery, and it's chapel is a little smaller, but equally gaudy, and easier to get to. Besides, Andechs has good food and beer.
I was a little let down with Dinkelsbühl, but maybe because I had just left Nördlingen.
Landsberg is pretty large, but still a town. It has some remnant of the old wall still standing. It also has the prison, which I didn't see, where Hitler started writing Mein Kampf.
Besides the tour of Harburg, I took the tour of the palace in Weikersheim and self-toured the Deutschesordnung Museum (castle of the Teutonic Knights) in Bad Mergentheim.
Weikersheim and Feuchtwangen were two smaller towns that I enjoyed seeing.