Berlin is not a picturesque city and does not try to be. Its sights are largely free, largely outdoors, and largely about the twentieth century — which makes it an unusually serious weekend destination.
The Wall, properly
The Berlin Wall Memorial on Bernauer Strasse is the one that explains it: a preserved section with the death strip, a watchtower, and documentation of what the border system actually consisted of — two walls with a patrolled zone between them.
Free, outdoors, and considerably more affecting than the alternatives.
The East Side Gallery is a 1.3 km painted stretch along the Spree — a good photograph and not an explanation.
Checkpoint Charlie is largely a reconstruction surrounded by souvenir stands. The nearby museum is dense and expensive.
The other free sites
The Topography of Terror — a documentation centre on the site of the Gestapo and SS headquarters, with an outdoor exhibition along a surviving Wall section. Free, and the clearest account of how the apparatus worked.
The Memorial to the Murdered Jews of Europe — 2,711 concrete stelae on undulating ground near the Brandenburg Gate, with an information centre beneath. Free.
The Reichstag dome — free advance registration required, with slots released weeks ahead and filling up. A glass dome with a spiral ramp above the parliamentary chamber.
Tempelhof — a decommissioned Nazi-era airport whose runways are now a public park where people cycle and fly kites on the tarmac.
Museum Island
Five museums on an island in the Spree, a UNESCO site.
The Pergamon has been undergoing extensive renovation with sections closed — check current status before planning around it.
The Neues Museum holds the bust of Nefertiti. The Altes Museum and Bode hold classical and Byzantine collections.
A day ticket covers the island and beats single entries.
The districts
Kreuzberg — Turkish Berlin, the canal, street art, and the bars.
Neukölln, adjacent and younger.
Prenzlauer Berg — the East's gentrified quarter, with Mauerpark's Sunday flea market and public karaoke.
Friedrichshain — Karl-Marx-Allee's Stalinist boulevard, and the club scene.
Charlottenburg in the west, with the palace and a different, older Berlin.
The two-day shape
Day one: Brandenburg Gate, Holocaust Memorial, Topography of Terror, Checkpoint Charlie in passing, then Museum Island. Evening in Kreuzberg.
Day two: Bernauer Strasse Wall Memorial in the morning, then Prenzlauer Berg or Tempelhof. Reichstag dome if registered.
Practical
Berlin is very large and the sights are spread out. The S-Bahn and U-Bahn are excellent and a day pass is cheap — factor in 20–30 minutes between districts.
Cash is still expected in many bars and smaller restaurants, which surprises visitors.
Sunday closes most shops, and it is when the flea markets and parks fill.
The airport is around 45 minutes by train to the centre.