I ski in Garmisch quite often as it is the closest and cheapest real skiing for somebody living in Berlin.
The Garmisch Classic area has great, steep, fast groomers as well as a fair amount of beginner terrain. The off-piste is somewhat limited but does exist.
The Zugspitze has a few intermediate groomers that honestly are not all that interesting. The off-piste is huge when it is in shape. It takes ages to get up to the glacier, and as a result I have only made the trip once. It is worth it just for the view, though.
So those are the two obvious places to ski from Garmisch, both relatively small but good enough for a day or two. Luckily there are a number of gems within about an hour of Garmisch (you can drive or take the train) that are even mostly included on the same multi-day ski pass.
Just over the boarder in Austria you have the Zugspitzarena, which is several smaller, not lift connected resorts. The best of the bunch is Lermoos. Great beginner terrain for your gf, and while the mountain looks small on the trail map, it "skis big". There is some great intermediate and advanced terrain on the mountain, as well as some obvious and very good off-piste.
In Mittenwald there is a small beginners ski area, not really worth the trip, but for experts you can take the Karwendelbahn cable car and ski the Dammkar, which is a 7km off-piste route. The patrol carries out avalanche control on the main route, although it is still advised to carry avi equipment. It's a fantastic run when the conditions are right.
Similarly Oberammergau also has a small beginners area and a single cable car, the Laberbahn, which also offers up an avi controlled off-piste route. It's shorter than the Dammkar but also steeper.
So there really is some great skiing in the area, you just have to be willing to travel a little bit each day to access it. The one big criticism of the area is the low elevation. In a bad year you can just about get skunked out everywhere but the glacier.
Garmisch is an interesting town. On the one hand you have the traditional Baverian village, but then there is the military presence. It creates a strange atmosphere, but I've always had a good time there.