The old abbey founded in 698 by St. Willibrord is one of the must-sees in Echternach. Today, it's a school building for high-school classes (7th-13th grade). The basilica next to it still serves as church of Echternach. If you're interested in the history of the monastery, there is a small but nice museum next to it.
The town square with its square cross and the historical guildhall "Denzelt" is a nice place to see and stay.
The roman villa about 20 minutes walk from the centre shows the remains of an ancient roman house. A walk-through is free, worth a visit.
The lake is an artificial lake. Enjoy the silence around it, 20 minutes walk from the city centre.