Go up into the Reichstag. It’s free!!! It’s going to be insanely crowded in the morning and early afternoon, but you can almost be assured of interesting people-watching while you’re in line. To avoid lines it’s a good idea to go in the late afternoon, but the best bet is to go after the sun has gone down. The city is lovely all lit up and during the summer heat, you’ll avoid baking in the glass dome. Get the free audio guide!!!
From the Reichstag, make sure you go around the corner and see the Brandenburg Gate. It’s iconic. It’s picture-worthy and there are always street-performers in front.
Walk around and through the Memorial to the Murdered Jews of Europe. Get lost among the stones. Visit the free museum that’s under the memorial.
If you’ve got some time on a Sunday head to Mauerpark. There you’ll find a rambling flea market crawling with locals and tourists alike. It’s busy, crowded and full of junk but I also think it offers one of the most honest pictures of Berlin. People of all ilk abound. Food and drinks are sold from little stands. Outside the market (if the weather is good) you’ll find families, couples, musicians, and groups of friends lounging on the grass. On one side of the park you’ll notice a mass of humanity gathered in the outdoor amphitheater. That’s Bear Pit Karaoke - an open air, open to the public songfest that happens every week. Grab a beer and join the crowds; it won’t be the best singing you’ve ever heard but it will be entertaining. (Ampelhead did a wonderful job covering this phenomenon a while back!)
Go to the East Side Gallery. This is so much more than graffiti. My suggestion would be to start on the Ostbahnhof side, walk the length of the wall and then turn right, cross the river by walking the beautiful Oberbaum bridge and follow the U-bahn tracks to the Schlesiches Tor stop. Wander this section of Kreuzberg - you’ll find delicious döner, coffee and eis and lots of interesting shops.
Go to one of the city parks - either the Tiergarten or Volkspark Friedrichshain. Excellent people watching. Excellent paths to wander. Excellent place to ride bikes. (Hey, take a Fat Tire Bike Tour.) Excellent spot to eat and drink. Just excellent.
Visit the Berliner Dom. Yes, it costs a few euros to get in, but you'll never see another Protestant church quite like it. Take the time to go down into the crypt. It's creepy, but interesting. If you can see a concert in the cathedral, that's probably the best way to fully take in the statues, the frescoes, the immensity, the organ, the beauty.