Most of Berlin's Christmas markets cost nothing to walk into. The exception everyone has heard of is Gendarmenmarkt's WeihnachtsZauber, between the square's two domed churches, which charges at the gate. That makes Berlin in December a cheap place to be festive, provided you watch the real costs, the food stalls and the bed. If New Year's Eve is part of the plan, book that bed first.
Even Gendarmenmarkt can be had for nothing. Entry has normally been free on weekday lunchtimes, except over the Christmas and New Year holidays, so time your visit for then. After dark, the market in front of Charlottenburg Palace is free, with the lit palace behind the stalls, and so is the one at the Kulturbrauerei in Prenzlauer Berg. The city's official site lists the rest.
On the coldest days, the Museum Pass Berlin covers more than 30 museums, Museum Island and the Jewish Museum among them, for three consecutive days from your first visit. The state museums shut on Mondays, so a pass started on a Saturday spends its last day outside the locked doors of Museum Island. Special exhibitions cost extra. Guides promising free museums on the first Sunday of the month are out of date; the city cut the scheme to save money.
The Berlin Wall Memorial on Bernauer Strasse charges nothing, nor does the Topography of Terror, and the East Side Gallery is simply a stretch of the Wall beside the Spree. The Reichstag dome is free too if you register in advance and bring the photo ID you registered with.
A 7-day AB ticket covers U-Bahn, S-Bahn, trams and buses, and groups should price it against the 24-hour small-group ticket, good for up to five. Either way, skip the Mitte premium. Anywhere a short walk from a U-Bahn or S-Bahn station will do.
The best-value market in Berlin is also the shortest. Alt-Rixdorf runs for three days on the second weekend of Advent, around Richardplatz, the old village square in Neukölln, and it is worth fixing your dates around. Entry costs nothing. Only charities and local groups may take a stall, and every stall is lit by paraffin or gas lamps, because electric light is banned.