My daughter will be in Giessen and Stuttgart next week and has offered to bring be back a small sampling of German beer. Any suggestions about what should I ask her to look for?
That depends on what kind of beer you like. IPAs and craft direction or Pils? Also, how long will she be staying? If she has a short time, she should go to a Gallerie Kaufhof, the biggest department store chain in Germany, where in their cellar supermarket section she can find most German craft beers and a few of the main (good) traditional styles.
I live in Stuttgart. You can get most of the best Bavarian beers over here (Augustiner, Ayinger, Hofbrau, etc), but some of it sits for months, so it may not be the freshest in the world. In Stuttgart, they brew Dinckelacker, but if you want some really fine (in my mind) fresh beers, look for Schonbuch. Any of their stuff will be great and is what i keep in my fridge
I had several of their Dunkel while in Tubingen a couple of years ago and it was indeed magnificent beer.
Whilst Schönbuch Bräu is ok - nothing exceptional and their Brauhaus in Böblingen is a really fun place to eat some great German dishes. My preference was Barfusser die Hausbrauere in Memmingen (15 min south of Stuttgart). Fantastic food and excellent beer. Plus you can experience Spreuerhofstraße, the narrowest street in the world. It's less than 13 in wide at the narrowest and less than 20 at the widest. Menu: https://www.barfuesser-brauhaus.de/memmingen/__Memmingen.html