Trier is potentially the oldest city in Germany, having been in existence since before 16BC, although Worms and Cologne also claim to be the oldest. It has an amazing amount of Roman architecture still standing, as well as a beautiful cathedral. The city's main attractions are a little spread out, so you might benefit from hiring a car in Trier to save time walking to each building. Those with an interest in more recent history may also want to visit Karl Marx' house, where the man himself was born in 1818. Trier is 5km from Luxemburg, making a change of scenery an easy option.
Trier is most famous for its Roman architecture, most of which is well-preserved and an insight into what life BC was like. The Porta Nigra, a former city gate, is one of the most impressive examples, but there are also the ruins of the Roman baths, which were the largest of their kind around the Alps. Trier also hosts the largest Roman festival in Germany every summer. It's where visitors will find the Holy Tunic, allegedly the garment that Jesus was wearing before he died; however, this isn't on display very often, so you're better off hiring a car in Trier and going sightseeing.