If you’re going to be in Berlin in the warmer months then make time to head out to Britzer Garden. It’s a bit of a ride (an uncomplicated one) but worth the travel. The garden is beautiful, huge and a perfect way to spend a sunny afternoon. There are cafes, a train to ride, a model boat harbor, lovely ponds, and fields for frolicking. The best time to go is in either May or October when the garden puts on celebrations of dahlias and tulips. In October you'd see these lovely dahlias (+ 10,000 more):
and in May, it's the tulips:
As for museums: If you’re only going to make it to one, go to the Pergamon Museum. Get the free audio guide and plan on being there a couple of hours. Everything in the museum seems over-sized. You’ll spend a lot of time looking up and stepping back to take it all in.
If you have time in your schedule, go out to Dahlem and visit the Ethnography museum. This museum is quiet and cheap; the collection is total eye-candy and wildly fascinating. I can’t sing it’s praises enough. Hey, while you’re in Dahlem, walk down the main street to the Botanical Gardens. There are a dizzying number of plant species in the greenhouses and the grounds are lovely.
Eat Eis (gelato). Eat lots of it. Try several different Eis places to find your favorite. If you’re in the neighborhood of Nollendorfplatz, stop by Fredo’s Eis stand - it’ll blow your mind and the service will make you smile.
If you’re in Berlin on a Saturday or Wednesday go east to Hohenschönhausen. It’s a former Stasi prison that provides perhaps the most eye-opening look at what life was like in the DDR. Most tours are led by former prisoners and though it’s a sobering tour, it’s absolutely worth your time. (English tours are only offered on Saturdays and Wednesdays - check the website for times.)
Eat well. Berlin is a great place to eat out because there's a little bit of everything and it's relatively inexpensive. I don’t usually like to recommend food (because inevitably you might not like it) but there are two restaurants we keep going back to and we think they should be added to your list of eateries! For Prussian-style German food go to Der Alte Fritz. It’s authentic, conveniently located at Alexanderplatz, not outrageously priced and there is English on the menu. Portions are huge. You won’t be disappointed. For Turkish food go to Hasir. (There are several locations around the city - I would suggest the one in Schöneberg so that you can stop by Fredo's on the way home for dessert.) These are the folks that invented döner and they do an amazing döner plate. Order a carafe of red wine, get the fried fetta appetizer, and when they offer you tea after your meal, get it! Come hungry and you'll leave full.