Pollok Park/Burrell Collection are also good. Pollok Park Family Day is 8th August and is good, but often very busy (we live close but walk!!). You get the train from Central to Pollokshaws West and its not far from there and signposted. Our kids love the Burrell Collection (fantastically eclectic museum) and the playpark there is good as well.
Gallery of Modern Art in town is good (right in the middle of the city centre) and there is also The Lighthouse close by, an arts centre that sometimes has good stuff on for kids. Second the Kelvingrove Museum recommendation - it has the Doctor Who Exhibition on at the moment as well - its costs to get into that but the rest of the museum is free and we really like it.
Depends on where you are staying. The underground is good for city centre/West End, but rotten for the Southside (where I live!) but there are good urban railway links and the buses are frequent but you do need to know where you are going!
There's a lovely park at Rouken Glen. Getting out of the city on the train is easy if you are heading to the Ayrshire Coast. On a nice day in the Summer we sometimes get a picnic, go to Largs, eat picnic, eat icecream, walk along the seafront and play on the (stony) beach, get fish and chips for tea and get the train home. Its very 'old fashioned' seaside resort-ish, but the kids love it (mine are 9, 7, 5)
For travelling around for a week on public transport you are best getting a travelcard from SPT - you can get one at the main train stations I think??? Can't remember!
Loch Lomond also nice - very pretty and more 'Highlandy'. Don't know how easy it is to get on public transport to Aberfoyle, but we love going there to Queen Elizabeth Forest Park - we can easily spen all day there in the pub woods!
Hope you have fun. We love living here, there is loads to do!