I took Qum Baby to a soft play centre that's opened up recently. It's located on falake safaye. Can't miss it, there's a man wearing a bear costume outside and handing out leaflets.
The place isn't very stroller friendly. It's in the basement and no where really to store them, but I managed to fold mine up and stash it under the shoe rack (umbrella strollers rock!) and said a little prayer to keep it safe.
It's 5000 tomans for an hour, which is about £1. There's a ball ball, lots of slides and ride on cars, play kitchen and other toys.
Qum Baby took a while to get into it, maybe since he'd just woken up from a nap, but he did love it towards the end of the hour. It's perfect for 1-3 year olds but older kids may find it a bit babyish. They had some craft activities and face painting too. Mostly mums there with their kids... A father did come but he didn't stick around. He did look a bit awkward being the only male over the age of 5 there.