I spent a few days there recently. The weather ranged from tolerable to awful but my planned stops were mostly indoors so no major harm done.
Yep, Battlefield Berlin is great. Even though everything can be found online too, it's just so fascinating to browse it all in person. Unfortunately (or fortunately for my finances), I only managed to reserve one hour for the visit, which wasn't enough at all. The contrast between its tiny store front and the shelves inside which go on forever is striking. One does not simply walk there, but Gneisenaustraße U-Bahn station (line U7) is about three blocks away.
From there, I tried my luck with
Modellbahnen am Mierendorffplatz, allegedly one of the best railway stores in the city. U7 takes you there quite conveniently in something like 15 stops and 25 minutes. It was well-stocked indeed, although very H0/N-scale heavy with nothing in O scale (for 28mm purposes, obviously) apart from a tiny bit of rolling stock. You can get almost any kind of scatter or tree kit ever produced there, though.
There are various Berlin WelcomeCards, which can buy you unlimited public transport and e.g. three-day access to the museum island. The discount is not massive but the concept was convenient for my purposes. Altes Museum has one large floor of Greek items and another of Etruscan/Roman stuff. Neues Museum has fascinating Egyptian things, "Priam's Treasure" (or whatever remains / has been replicated after Soviet looting), old German history, and many floors of stone/bronze/iron age exhibitions which get quite exhausting after everything else. Nefertiti's bust is neat but maybe hyped out of proportion.
Pergamonmuseum is currently 2/3 closed and even the Ishtar Gate and Market Gate of Miletus are partially covered by ugly scaffolding. It makes the place mercifully fast to visit, however. I was happy enough when I found the Assyrian water basin with priests of Dagon in fish costumes sprinkling water:

(I painted one such priest for
LPL8 ancients round as a clever transition between cultists of earlier rounds and fishmen of later rounds. Even the shields were Dagon-themed. I still don't know if anyone got the reference.)
Visiting every exhibition of the the island museums, even briefly, will probably take several days so plan and pick accordingly.
Brandenburger Tor doesn't offer much more than a billion tourists and a mile of souvenir shops. Checkpoint Charlie is along the route to Battlefield Berlin (U6). There is also a Berlin dungeon in Mitte, which I skipped due to lack of time and it looking like a cheesy tourist trap. I may be wrong, of course.
Currywurst keeps you going but I actually preferred a Weihenstephaner biergarten (fully aware of the fact that the brewery is really in Munich area and the place thereby Bavarian-themed). Every variant of Berliner Kindl I sampled was poor in comparison. I guess it's OK with currywurst but nothing to write on LAF about.
Anyway, it's a huge city with a lot more in every direction. Even well-known essentials may be >10 km away from the centre. You have to prioritise heavily, based on your preferences. Fortunately the place is notably tourist-friendly and well-organised*. Deciding where to go is the difficult part. Getting there is usually easy. Any kind of food and drink is available basically around the clock for reasonable prices (from a Nordic perspective) so you shouldn't have other problems with that either than choosing. Note that shops (such as BfB) are closed on Sundays. Reserve that for museums, strolling or something similar.
Very lively city. Would visit again.
*But seriously, they should get their act together with the airports, train service and museum renovations...