First time in Berlin

I may be biased because I work for Hyatt, but the Grand Hyatt Berlin is terrific. Close to the park and main train station, and a block from major subway connections and a nice Rewe grocery store. Most importantly, the rooftop (indoor) pool and hot tub are to die for after a long, cold day of sightseeing!

I had a very good experience with this hotel a year ago. My room had a kitchenette and extra space. I think they also have two-room suites that might work better for your family. The location was excellent, a short walk to Museum Island, Alexanderplatz, the Jewish Quarter, and the U- and S-Bahn trains. No charm, overpriced breakfast (but bakeries and cafes a block away), but clean and comfortable enough, with a friendly and helpful front desk.

The Adina chain has other hotels in Berlin. While I haven't stayed, I assume they're all similar, so you might prefer one closer to whatever Christmas market appeals to you.

Don't miss the Pergamum Museum.

Don't miss the Pergamum Museum

Unless your only reason for going is because it's highly rated as a must do in Berlin - personally I have never had any interest in the Pergamon.

CAVEAT from https://www.visitberlin.de/en/pergamon-museum

Please note that the museum’s premises are closed due to renovation work. The central building with the Pergamon Altar as well as the north wing will reopen in 2025 at the earliest.

A new, temporary exhibition building is located opposite the Museum Island: the exhibition "Pergamon Museum. The Panorama" with the 360-degree panorama by Yadegar Asisi and antique originals from Pergamon makes it possible to experience the Pergamon Altar in its original form and in its urban context on the Acropolis.

My husband, adult daughter and I just spent a week at the Circus Apartments in Berlin https://circus-berlin.de/apartmenthouse/. We stayed in “The Walter” a spacious, modern, two bedroom/2 bath apartment with a full kitchen and large living area with sliders to a balcony overlooking a courtyard. One bedroom had two twins and the other had a queen-sized bed. The immediate neighborhood was residential and quiet with restaurants, shops and good transit connections just a block or two away. We walked to a lovely Sunday Flea Market at Arkona Platz. The Hackescher Markt was an easy 15 minute walk. Note: There is an affiliated Circus Hotel and a Circus Hostel a few blocks away.

The Panorama mentioned upthread was one of the highlights of our visit to The Museum Island.

I agree with Dick, the Adina Hotel at Hackescher Markt is a great place to stay. It is close to Tram, S-Bahn and U-Bahn stations as well as museum island. Our room even had a washer and dryer for laundry. There is a Rewe grocery store around the corner plus a nice little bakery next door.
I don't know about nearby Christmas markets but the proximity to transit will make getting around Berlin quite easy.

Jay

We've been to a lot of Christmas markets, but Berlin's Gerndarmenmarkt remains a favorite. Really beautiful.

I will also recommend Dick and Jay's rec for the Adina Hotel Hackescher Markt. I was a solo traveler there in May and stayed in a studio apartment. The prices are reasonable and the hotel was very nice with many amenities. Plus the location cannot be beat. You are very close to major sightseeing, and there are quite a few good restaurants in the area, along with the Rewe grocery, as Jay mentioned. I would definitely stay here again.

Thank you, everyone for the suggestions.