Metz, France - where else to visit in a week?

Metz is quite near the Art Nouveau city of Nancy, which is less than 40 minutes away by local train (no need to book in advance). Strasbourg with its picturesque historic center is also not terribly far away--about 50 minutes by TGV (booking in advance may save considerable money). South of Strasbourg are Colmar (pretty, though touristy, historic center and the very good Unterlinden Museum) and a string of cute little wine towns. If you want to see the little towns, you will benefit greatly by having a rental car. Otherwise, some can be reached by bus, and distances are short enough that an occasional taxi might not break the bank. But a car will be a lot more efficient.

I see that Trier, Germany, is also within range. I haven't been there, but it's often recommended.

You are also very close to the Lorraine American military cemetery which has the largest number of our WWII casualties. Definifely worth several hours for all of you.

The Centre Pompidou in Paris built its first satellite branch in Metz a few years ago. It has a selection from the permanent collection plus special exhibitions. Fair warning: This is "contemporary" art which some might think weird. But since you are there, it's worth a few hours to see what weird means. I liked it, but I like its home in Paris too.
https://www.centrepompidou-metz.fr/en/welcome

Metz is a pleasant place, starting with its train station, considered of interest both for its looks and because it was a project of the Germans when they were in charge. Nice city centre with a cathedral. Because of its nearness to both Germany and Belgiium its cuisine is northern, including good places to drink beer.

http://www.tourisme-metz.com/en/home.html

We found Verdun interesting, but we are history oriented. We stayed in Nancy, and loved it. Nancy has much art nouveau in the architecture and museum. It felt like a little Paris to me. Over the Vosges Mountains are little half-timber/stone, wine oriented villages that we enjoyed.

You can also visit the forts of the Maginot Line. I visited two years back the huge fort Hackenberg east of Thionville and west of it fort Fremont seems to be comparable and worth going to too. An underground narrow-gauge railway train brings you to the different locations. https://www.maginot-hackenberg.com/?page=home

The Völklingen Ironworks is a UNESCO World Heritage site, located some 60km east of Metz.

If you like crystal, Baccarat is about 1½ driving from Metz.

Many many wonderful places are relatively nearby:
Trier (Roman Ruins), the Moselle Valley, the castle-filled stretch of the Rhine between Koblenz and Mainz, Heidelberg, the Black Forest region of Germany just east of Strasbourg, etc.