There are quite a few options for parking in Maastricht, all of which can be reviewed on their handy website.
Here is my opinion on some of the options available.
Park and Walk
Cabergerweg – Cabergerweg, Maastricht
€1,50/hour up to €6/day
About a 10 minute walk from Vrijthof for Markt Square. You don’t drive into the city, so you avoid all of the traffic. There are 3 Park and Walk lots available, but this one seems to be the closest to city center.
Vrijthof – Vrijthof 100, Maastricht
€3,53/hour or €35/day
It’s an easy drive to get to this lot in the morning, but the lot fills up fast once stores open. It’s also extremely expensive, so I wouldn’t use this lot if you plan on staying for a long time.
De Griend – Griend 4, Maastricht
€2,14/hour or €12/day
This parking garage is on the opposite side of the river from city center, near the train station. This means a lot lower chance of traffic. It is located right next to a bridge that takes you to Mosae Forum and Markt square. There are stairs that you must climb to get onto the bridge, but that is the only down side.