Take a boat trip on the River Spree -
link here.
I have taken them going east from the centre towards Köpenick (nice old town centre, popular on a Sunday) and the Grosser Müggelsee lake, but they also run westwards towards Wannsee.
Go up the TV Tower (Fernsehturm) on Alexanderplatz. Beware of waiting times at busy periods, though if I recall correctly you can buy them in advance for timed slots.
Eat Currywurst from a street stand (not fine cuisine, but fun - once).
Another favourite of mine that gets less attention in tourist guides than I think it deserves is the enormous Soviet war memorial (Sowjetisches Ehrenmal) in Treptower Park. It's maybe not so impressive for small children, but you could always try and interpret the characters and themes on the array of neoclassical friezes on the huge marble panels that line the way to the monument.