Volklingen
by antistar
A few minutes out of town is the magnificent rusting hulk of a disused ironworks, now a UNESCO protected site. The heart of Saarland is its industrial heritage, and you won't find it better preserved, exhibited or manifested any better than in Volklinger Hutte. In fact, you'd be hard pressed to find a better example of a 20th century industrial landscape anywhere in Germany or even Europe. It's a quality site and well worth a visit.
To get there, just take a local train from the station in the direction of Trier.
Alte Sammlung
by Nemorino
Here there are actually two museums, one for older art works (up to and including the 19th century) in the former Schiller School and one for contemporary art by regional artists, right next door. In the space between the two museums they have built a modern entrance hall for both of them.
Admission was free when I was there, because parts of the older museum were being renovated so two of the floors were not accessible. But I believe they will again charge a small admission fee (it says EUR 1.50 on their website) when the renovation work is finished.
Second photo: The former Schiller School, now part of the museum Alte Sammlung, with a piece of modern sculpture in front of it, or rather the kind of sculpture that was considered modern several decades ago.
Saarbrucken
by smirnofforiginal
Saarbrucken is the capital of Saarland which is a very modern city but was once a royal residence (under Prince Wilhelm Heinrich 1718-1768). It's a relatively compact city, with many good restaurants and bars and is split in two by the River Saar.
(a bit of history...Saarland enjoyed Celtci & Roman times. Then throughout the middles ages France governed it. In 1815, after Napoleon was defeated it was divided by Prussia and Bavaria. After WWI, under the Versailles treaty Saarland became an independent territory and was ministered by the League of Nations with a bit of help from France. In 1935 the people of Saarland voted to rejoin Germany. Then, again, after WWII, Saarland became a self-governing region under French administration until 1955 when it was returned to Germany).