Berlin is an amazing city, we lived there for 4 years and never got bored!
I would take them to the east side gallery (basically a large part of the remaining Berlin wall by the river which is covered in various artworks). The closest train station is Friedrichstraße - there is a cool art gallery really close to there too called Urban Spree which is an industrial area covered in graffiti which is just an interesting place to walk around (and look out for the vintage photo booths!) - some weekends there is also a great flea market there and lots of excellent restaurants nearby. Then from there you can walk over the Friedrichstraße bridge to Kreuzberg, another area with great food and interesting shops. You could just walk around Berlin looking at all the street art and fill a whole day.
Other areas which I recommend are Prenzlauer Berg (in particular Mauerpark is an interesting place to visit at the weekend you can watch karaoke and there are often graffiti artists working on large artworks on old bits of the Berlin wall there). There is also Bernauer Str nearby where there is an excellent outdoor Berlin wall exhibition. There is also all the usual tourist type stuff to do - museum island, get a boat tour down the river to see the parliament buildings, the holocaust memorial near the American embassy is definitely worth a visit and the Reichstag.
Also Tempelhof Airport is a really great place to go on a weekend - it's a closed down airport but they've kept the runway area as a park and you can go and watch people roller skating, dancing, playing cricket on the runway etc. It's a cool place to hang out.
I probably would try to stay somewhere like Prenzlauer Berg or Kreuzberg or Friedrichstraße rather than right in the centre as they are more relaxed and loads of good breakfast or brunch places nearby.
It's a really easy city to travel around, but if you buy a paper travel ticket make sure you click it in the machine on the platform before getting on a train/tram as you'll get fined if you don't and there are loads of ticket checkers, especially on the trains from the airports!
Enjoy your visit, I can't wait to go back!