3 days in Berlin

Berlin has so many sights spread out across the city. There is no "historic center" the way there is in many other cities. You will almost surely want to rely on public transport, which is excellent and easy to use.

I stayed in Prenzlauer Berg, and I liked it. But I can't say it's the best neighborhood to stay in, because it's the only neighborhood I stayed in. I know many visitors like staying in Mitte or Kreuzberg. But I think your best bet is to look at a map and read about the different neighborhoods. Search Google for best neighborhood to stay in Berlin and see which ones most closely fit your vibe.

Choose any hotel along the central S-Bahn axis between stations Warschauer Strasse and Charlottenburg:
https://sbahn.berlin/en/route-map/

Public transport is fast and cheap.

Here is a touristic overview map of Berlin districts with descriptions. Be informed that the districts are as large as cities on their own with often very heterogeneous neighborhoods - called Kieze. Sometimes one or two blocks or a large street make the difference.

Avoid apartments because it can happen that between booking and arrival an apartment will disappear (order by authority) and you end up without accomodation. Nearly all apartments in Berlin are illegally rented to tourists.

The idea in #1 makes no sense imo because oh-oh does not know what your definition of "best" is.

So, if you give us more criteria we can help better: lively / silent, young / mid-age / older, modern /classic, ...

I'd start by going to Google Maps, entering the names of the top sights I wanted to see one by one, and clicking "Save". The map will clue you in if you have a significant concentration of sights in one area. Berlin is large, it has many worthwhile sights, and you don't have much time. It would be a shame to pick a hotel that requires substantial travel back and forth every day.

Don't miss the Pergamum Museum.

The Pergamonmuseum is completely closed due to construction work. Pergamonmuseum - Das Panorama remains open.

When I was in Berlin in 2022, I stayed in Hackescher Markt, at the Adina Apartment Hotel Hackescher Markt. My room was a large studio since I was by myself but they also have 1-2 bedroom apartments with fully equipped kitchens, washers and so on. They do have hotels in other Berlin locations as well, but I personally really liked this location. The staff was friendly and courteous, and the rooms were very well prepared, large, clean and nice. Breakfast is available although given the kitchen facilities, I just ate in my room in the morning. And the price was quite reasonable and I would think within your budget.

The hotel is very convenient to the U-Bahn, S-Bahn, and trams, and is an easy walk to the major museums. The DDR museum is only a few blocks away, along with the TV Tower, and Museum Island is a quick 5 minute walk. You can easily walk to Lindenstraß from there, There are several grocery stores a few blocks away along with a couple of wine shops, many cafes and good restaurants. I would definitely stay in this location again.

Check out this Forum post for ideas. https://community.ricksteves.com/travel-forum/germany/what-was-the-best-thing-you-did-in-berlin

I really appreciate everyone's contributions - thank you!

I'm thinking we might defer our trip to Berlin until we have considerably more time to do it justice. Because Europe is - at best - a 24 hour trip from New Zealand, we tend to try to fit too much into our month. Berlin may just have to wait ...!

Contact Jeremy Minsberg, theberlinexpert.com. He is the guru on Berlin and area and will help you plan a wonderful time.

Berlin may just have to wait ...

I think it is a good idea. Maybe next time you will find a month of travel which is not winter in Berlin. Then the possible choices are even more.