I have not been with kids, only as part of work trips a couple of times. Ace place!
The street art is great - there are lots of online guides to find them, and they do seem everywhere in some areas.
I also enjoyed the market at Balti Jaama Turg - great food, some local crafts, hip and trendy...surrounding area has great cafe, street art, bars and music going on.
I have run out to the Linnahall a few times - old nazi u-boat pens, but then I remember them from Alan Walker videos, so think they are cool...
I took the bus one evening out to a beach (Pikakari?) which was a lovely picnic on an August evening....nice woodland walks around some of the beaches. Public transport is slick and cheap - you can go some real distances.
You can do a day trip to Helsinki!
There are some brilliant public saunas, but not sure the kids will get in.
The highlights for me though was getting out the city to swim in the floating bogs, swim in the Baltic (nae as baltic as Scotland), the bars and, ahem, some of the nightlife as a newly single person on a work trip. whistles.
Be VERY careful of the pick pockets. They were rife.