Re: river cruise you can go on one of the large boats or hire a small motor boat for the family.
We did the latter and took a picnic on board with us - had a lovely time and the kids enjoyed driving the boat (obviously "thinking" they were driving with heavy supervision). It's not a great option in bad weather though.
In addition to Museum Gardens I'd also suggest Rowntree Park (20 acres of park near the river in the centre of the city).
In many ways York is just a great city to walk around in and soak up the sights and despite the inevitable queues I'd definitely recommend a visit to Betty's Tea Rooms for afternoon tea (and don't be disappointed/reject eating downstairs - most people queue longer for the ground floor dining area, but I think the basement dining room is far more elegant and 1930's with beautiful wood panelling). It's not cheap but the food is lovely and they have brilliant child friendly food (DS is a food nightmare and the staff arranged an "afternoon tea" for him on a cake stand with a layer of toast, beans and ham sandwiches
).
There's some beautiful buildings and many lovely restaurants.
The Minster is spectacular and worth a look even if only from the outside - they used to do tours to the top of the Minster where the views were spectacular (not been for a few years so not sure if they still do them).
Only one word of warning from when we last visited.
It's turned into a bit of a hen/stag destination so on Friday and Saturday evenings I'd generally avoid the main city centre and stick to the perimeter of the city (though according to relatives who live there - which is why we have visited York many times - the Council and hospitality industry have been clamping down on this so it might be better now). For example there were some lovely places to eat/hang out/shop on Bishopthorpe Road (near Rowntree Park) that are free from the hen/stag gangs.
Have a lovely time!
We are hoping to visit again this summer to see our relatives and enjoy the city!