Stay Jordaan neighborhood. It's near the Anne Frank House, and has easy access to other sites, but it's still mostly working class residential. Restaurants, pubs, and ice cream are all cheaper there.
Alternatively, consider staying in Haarlem. Price the commute to Amsterdam before you decide.
Price renting an apartment as cooking-in and packing lunches will also save you money. But if you are traveling solo the apartment might not be the cheapest option. Even in a hotel, cheese, crackers, fruit and sausage is a good lunch option. Buy them in groceries outside the tourist zone. If you are staying in a hotel consider making lunch your main meal and saving the cheese and sausage for dinner. Buy your beer at a grocery store. Drink it at the hotel or apartment.
Get one of the museum passes. Price the options. The Amsterdam Card is better if you won't be daytripping and the Museumkart if you will be.
Daytips cost train fare, but often little else especially if you have a Museumkart. If you are going to day trip, do buy a train/bus card and do budget time to cash it out at the end of your trip. Making your meals out day trip meals. If you will not day trip and are staying in Amsterdam, you can walk everywhere if you are energetic.
I'd suggest a bike day, except that sounds ungodly cold in December.