I'm a long time Berlin resident, I've posted on this subject under various names many times, so you could try doing an advanced search.
But adding to what people have written in here, filling in the gaps:
You can get an all-inclusive travel ticket for a number ofdays which is excellent value, and includes discounts for lots of attractions. They're sold at both airports.
Many of the museums are world class, so you really need to think about where your interests lie and specialize: history or art or science? One of my personal faves is the natural history museum. The trip up to the Reichstag dome is free and worthwhile, but compulsory reservation means the spots disappear quickly in summer.
You can get a 24-hour ticket for all (most state run) museums, but you will get fed up quickly if you go to more than three (bitter experience). It's best to attempt those on Museum Island together, but bear in mind that much of the Pergamon is closed off for renovations (including the eponymous altar I think).
The weather is verrry weird at the moment. July/August here tends to be like New York - hot and sticky daytimes leading up to frequent thunderstorms in the late afternoon. The difference being that virtually nobody has air conditioning
. But it's mercifully pleasant right now - breezy and about 25 degrees, which is perfect. The best local weather forecast (sadly German only) is from RBB online ( give in RBB Wetter).
Bear in mind that Berlin schools are starting back very early this year - in fact tomorrow - so the city will be full of tourists PLUS locals, and public transport can get very full of kids around 7.30 am and 2pm ish.