
In previous years the following restaurants have been offering dinner for under €100 per person. It's likely they'll be doing the same this year. They are all highly recommended.
Schuhbeck's Südtiroler Stuben - located on Platzl next to the Hofbräuhaus, this would probably be my own first choice if I were in Munich this year. Three course meal for around €60, or €80 for four course - not including wine.
Trader Vics - seven course Polynesian food in the basement of the Bayerischer Hof hotel. Costs around €90 per person.
Le Sud - one of the best French restaurants in Munich. Located in Schwabing, the night here will be relatively quiet but very pleasant. They are taking NYE reservations right now.
G-Munich - the website says that they have "Betriebsfeier" for the week over Christmas and New Year. I suspect they'll be open on New Year's eve though. Last year they were open and serving a seven course meal plus champagne. Nice atmosphere. Phone to confirm.
And if you feel like splashing out, try either the Four Seasons or the Mandarin Oriental hotels - both have NYE dinners from around €225 per person.