Just rent a bicycle and go exploring the city!
The Casemates of Maastricht are underground tunnels which were used in historical times to defend the city.
Maastricht was a important city, it was the entrance of Holland in those times! Many battles have taken place in and around the casemates of Maastricht.
I just came back from my 10-day trip to Budapest. Pointless to say that I totally loved it!