We'll be in Munich 24 December through 27 December and we're trying to find the best place to stay that a) won't break the bank (130 euros at most!) and b) allow us to have something to eat on the 24th when everything will be closed. I'm thinking of hotels with a restuarant, but which one? Places near the Viktualienmarkt were recommended, but which ones? If any?

Check hrs.com for hotels. That should steer you away from the 3-5 usual suspects that will probably charge dearly during those days.
You can set the filter to list hotels in increasing distance from Marienplatz, the historic city center of Munich.

Hotels in the vicinity of the central station are usually much cheaper than in the pedestrian zone/ historic center(which is only a short stroll away).
The neighborhood may not be as cosy as Viktualienmarkt, but a far cry from being seedy or even dangerous.
You can expect to get a double room in a 3* hotel for €60-90.
Also several 4-5 star hotels are in that area, as a fall back option for dinner on Dec 24.

Btw.. not all restaurants are closed on Dec 24. You won't starve to death even when your hotel does not have its own restaurant. The better hotel restaurants usually have special or thematic X-mas dinners on Dec 24, so while availability is there, you may be "forced" to splurge more on a fine 4 or 5 course dinner than on a regular a la carte dinner.

I have looked at places near the train station and I guess my concern is the 10-15 minute walk or even 20 in the freezing weather. I've traveled in Spain, France, and Italy during warmer months and walking 2 miles wasn't a big deal. But I recall waking two blocks in Chicago in January and it felt like an eternity.

Do you still think the stroll from the station to the town center is ok? I'll wear a heavy coat, hat, etc., but I'm kind of a *freezing* weather weakling.

You can take the underground suburban trains every 2-3 minutes from the central station to Marienplatz. Since the historic city center is mostly a pedestrian zone, you will have to walk anyway, eventually.

The historic city center starts 500 meters east of the central station, so it's not an "off-center" location.

In addition, you may want to explore other sights that are not in stone's throw range of Marienplatz, e.g. the museums, Nymphenburg palace, etc.. all of those require some form of transport and walking anyway.
Except for Hofbräuhaus, the Residence and Viktualienmarkt, I would not know any other sights which make it a logistics advantage to stay very close to Marienplatz.

At night, the historic city center is not one of the hot spots (at least not for locals) to have dinner. It gets surprisingly deserted. You may want to take the train to Schwabing or Haidhausen district for a little change from the Schweinebraten and dumplings fare at the beerhalls. Or explore the Gärtnerplatz neighborhood just a bit south of Viktualienmarkt.
All of those can be reached as easily from Marienplatz as from the central station area.

December is usually more mild or cool than bitterly cold. Daytime temperatures above freezing are the norm and a "White Christmas" usually the exemption from the rule, unfortunately.

I have stayed (twice) at the Hotel Schlicker, which is just outside Marienplatz and 'behind' Viktualienmarkt. We would stay there again. The location is very good IMHO. The breakfast was very good. We got an internet rate that made it affordable (for us.) Don't miss the Assam church, which is walkable from there. Have a great time.

I just checked the Schlicker and they are booked from the 22th thru the end of the year. Sorry!

We have stayed several times at the http://www.hotel-am-markt.eu/, which is literally on the V Market. Doubles start at Euro 98 if I recall from our last stay. It's not a glitzy place but it's clean, quiet, comfortable and the location is as good as you can get near the VM and Marienplatz. Check out the on-line video.

pef - That looks good to me. I remember seeing it and the location is great! I may try it next time.

We have always stayed at the Hauptbahnhof area and have been to Munich a half dozen times in mid to late December. We find it convenient and a good value.

We like Sofitel Bayerpost and LeMeridien (generally available via a bid on Priceline for a good price). We booked Sofitel for this years visit, arriving on December 28th. Eurostars Hotel is a newcomer to the general area and can be a great value.

We walk everywhere from this area; if it is too cold or far for your preferences public transport is excellent.