Berlin is awesome, so much to see and do. Mostly historically things here, but there are plenty of light entertainment / art galleries etc that we ran out of time to explore!
We stayed most recently at the Berlin Marriott Hotel, just a short walk from the Brandenburg Gate, and minutes from Potsdamer Platz, which connects you very well on the U-Bahn and S-Bahn. Lovely stay there.
Rausch Schokoladenhaus
This is a must visit! Lovely chocolate, a great cafe, and amazing chocolate sculptures!
https://rausch.de/en/pages/schokoladenhaus-berlin
Visit the Bundestag
Interesting tour and you can see for miles from the top of the glass dome.
https://www.bundestag.de/htdocs_e/visits
Bradenburg Gate
A hub for people gathering - have a look at night as it is all lit up and looks very pretty.
Treptower Park
A bit further out if you fancy a trip. Biggest Soviet war memorial - quite awesome in the 'awe' sense of the word. It is intimidating huge!
http://www.visitberlin.de/en/spot/soviet-memorial-treptow
Tiergarten
Main park, near Brandenburg Gate - lovely walks.
Holocaust Memorial
Hard to miss this as it's quite large and in the centre, worth a look, poignant memorial you can walk around/ through/ get lost in.
https://www.tripadvisor.co.uk/Attraction_Review-g187323-d617423-Reviews-The_Holocaust_Memorial_Memorial_to_the_Murdered_Jews_of_Europe-Berlin.html
Willy Brandt Museum
Good (free) museum about an interesting chap: https://en.wikipedia.org/wiki/Willy_Brandt
http://www.willy-brandt.de/en/forum-berlin.html
Stasi Museum
This place is very good, well worth a visit if the topic interests you. Looks like an ordinary office block, but it's full of atmosphere, it's like stepping back in time to some tinker tailor soldier spy moment!
http://www.stasimuseum.de/en/enindex.htm
Checkpoint Charlie Museum
A bit more touristy than the other museums but we found it was a good overview of the history of the city.
http://www.mauermuseum.de/
Berlin Wall
Has (obviously) been knocked down but there are still pieces up to show the scale of it, and gold markings on the road to show where it ran.
East of the city
Head over there for different architecture, a more Soviet vibe and other delights. For example, they still have the old style traffic lights where the 'man' wears a hat.
https://en.wikipedia.org/wiki/Ampelm%C3%A4nnchen
Unter den Linden
A nice pretty tree-lined road, which the Brandenurg Gate is at the end of. Bit like The Mall in London. Some nice restaurants along here
Food
In general is easy to come by and delicious - everywhere we ate was nice, and the food was good quality. Waiting staff were very friendly to our 4 year old. Be prepared for lots of sausage, potatoes fried with bacon and sauerkraut, but there are other cuisines catered for too, and probably some healthy options if you look hard enough!
Getting around
Although the metro is cheap and quick, I would say save that for longer trips and walk as much as you can, as the history really is everywhere for you to see!
Airports
We flew into the Berlin Brandenburg airport on our most recent visit. It was very easy to get to the centre from there on public transport.
Enjoy it, it's a fantastic city.