On a hill overlooking the town there is a large castle, Veste Coburg, from which you can see an amazing view of the city and surrounding hillside. Housed within there is a museum. It is also the location where Martin Luther stayed while being declared an Outlaw by the Holy Roman Empire.
Schloss Rosenau, the birthplace of Price Albert, Royal Consort to Queen Victoria is just a couple of miles North East of town.
Visit Castles and Palaces. Wander the Midevil Markplatz. Walk the path of original walls of the town. Wander the park around Veste Coburg.
Bamberg and Nurnberg are both good destinations for a day trip from Coburg.