First a note: the week numbering thing is not done in the English speaking world. It really confused me for quiet some time after I moved to Germany. Now I see it as an effecient way to express time, and I wish our American business partners used it. Anyway, you're talking about the Christmas/New Year's week and a late February week.
My one trip to Garmisch was for Christmas New Year's last year, and I will be returning for a weekend this January.
I'll try to offer some insight, but last year we had historically poor snow conditions, so I certainly did not see the best of the place.
In the Classic Area (directly in Garmisch), the Kandahar is one hell of a fast run. It's great fun so long as it isn't crowded. Lap it for an hour or so first thing in the morning, then move on. Little else was open when I was there, but from what i can tell the best stuff was up around the Alpenspitz area. The Hausberg area was dull and full of kiddies following their instructors like ducks.
The Zugspitze was in awful shape, which is certainly not the case now. The pistes (or rather the one that was open) were narrow, icey and crowded. The areas off the piste were massively dissorientating (as expossed glaciers tend to be) and all the more dangerous given the conditions. I'm conviced that with someone who knows where to go, it would be great. Otherwise it is just nerve-racking.
Just over the border into Austria (included on your multi-day lift ticket). Lermoos was really quite good. Berwang was mostly dull except for a double chair on the far side of the village that accesses some pretty nice terrrain. Doing laps on that is a nice way to spend a morning.
In Mittenwald (also included on your lift ticket) is the Dammkar. A 7km unpisted but avi controlled run. It was closed all last year due to the lack of snow, but I'm looking forward to hitting it this winter. It should be very good.
The Dammkar is probably your best bet, along with the Zugspitze off the pistes. Lermoos and Berwang looked as though they might have been promising had there actually be any powder last year. But they did not, so I can't really say.
The town is full of traditional Gaststüben serving great food. Just walk down the side streets and follow your nose. On mountain, I had a great meal in a hotel at the base in Lermoos as well as at a restaurant on the observation deck on the Zugspitze (Germany's highest beergarten!). I'm sure there are tons of other great places. Partenkirchen is more quaint, Garmisch is more cosmopolitan. We also had an outstanding dinner in Mittenwald. Hotel Post, I think it was.
The Classic Area has tons of huts that get rocking in the afternoon. Otherwise, there is a great place at the base in Lermoos (Lahrme Ente). If you ski the Zugspitze, get off the cog wheel train on the way down at the midstation and ski the single run down to Eibsee. At the end of the run there is the 'Eibsee Hütte'. It's tiny, but great. If you take the cable car down is not too far from the valley station, as well.
If you are going in week 52, you will be there for the New Year's ski jumping. It will be crowded, but it will also be a massive party in town and on the slopes, especially in the Classic Area and especially on the 31st. There will be events on the town square most evenings, including I believe a cross-country race. I did not ski the Classic Area in the afternoons because it was so crowded (instead hopping on a train around 11:00 and heading over to the Austrian resorts), and there was a fairly high number of people drinking heavily on the 31st well before noon.
Garmisch is like a museum. It's really interesting. Mittenwald is also a very beautiful mountian village. I would also recommend visiting the Ettal Monestary (they have a brewery, too) and Oberammergau.