Hamburg

The xmas markets officially open on Dec. 1st, you probably know this already. I assume that there will be an opening ceremony of some sort but I don't have any details of this. If there is one then it will be at the Rathaus.
Gluhwein is what is most commonly drank but you also have to try out the feuerzangbowle. There's usually only 1 or 2 places doing this, last year there was a tent at Jungfernsteig in front of the lake doing it, probably be there again. You'll know you're in the right place when you see a large copper pot and a guy burning a large block of sugar with a flame just over it. Perfect remedy for the cold weather

I'd usually recommend the boat trips from Landungsbrucke, especially the one around the old Speicherstadt but it will be very cold, it's already cold now. Landungsbrucke (U3 u-bahn) is the main harbour area, nice for walking around but a bit cold at this time of year. You can also get sightseeing bus trips around the city from here, these are informative and help you get to know the city. You can hop on/off any time you want.

Maybe a trip to the Dom (it's across the road from u-bahn stop Feldstrasse (U3), or you can walk from St. Pauli), it's a large carnival, plenty of rides and can be fun. They have a nice open cabin structure with lots of tables and benches with open fires inside. Nice for sitting and having a few beers. They also have a large firework show at the weekend, forget if it's Friday or Saturday.

Not sure about the shopping on a Sunday, shops are normally closed on Sunday but there are exceptions now and again, I've yet to figure them out. They might be open on that weekend with the start of the xmas markets, but I'm just guessing here. As for shopping, Monkebergstrasse would be the main shopping street. The big stores Saturn, Karstadt and the Europa Passage are on this street. There is also the Alster Haus at Jungfernsteig, you can get to this by walking through the Europa Passage and crossing the street to the left, across from the lake. If you exit the Alster Haus through H & M you will come out on the street where a lot of the designer stores are, this is behind the Rathaus. Can't remember it's name.

Schanze also has some good shopping, more alternative. I actually prefer shopping here but it's down to personal taste. You can get there on the u-bahn (U3) or s-bahn (Sternschanze stop). Schanze also has a few really nice little places for eating and is a good spot for going for drinks in the evening. Another area for going out is the Reeperbahn. I've never eaten there but I can imagine it wouldn't be the best as most places are aimed at tourists. The Reeperbahn offers a very broad range of entertainment, theaters, musicals, live gigs, bars, strip shows (both classy and seedy, Dollhouse would be the best, 50/50 men/women customers in there and good fun), discos, transvestite shows (good fun if you're up for it, Pulverfass is the name), discos, brothels, etc...

Can't really think of eating places around the city, I usually stick to a few places near where I live that are really nice. There's a really nice Argentinian steak house beside me but it's about 10 mins out on the u-bahn from the Rathaus.

My biggest tip would be to but a group ticket for yourself and the wife. Can't remember if it's called a 3day ticket or a weekend ticket but you can then use all the buses and trains for the weekend for getting around.

Have a look through here for more ideas/tips for Hamburg.