In Bramley there is Active Tots which is a soft play place in a converted Barn. It's for tiny children only. DS is 3 and too old for it now, but we used to love it - good cafe too.
There's 2 indoor play centre's for older children - Playdays in Lychpit and JJ's nearish to town. Both are good and have areas for smaller children.
Mumbaba on a friday at Christchurch on Reading Road in Chineham. Run by Joy - who is a legend round here. It's a singing group - turn up and join in - at 9:30am and at 11am. Costs £3.50 and includes drinks and biscuits.
Joy also runs Zingtastic on a Monday at the same times as above at St. Gabriel's church in Popley.
If you go to Christchurch any day mon-thurs, there's a secretary called Ruth who has an office in the entrance hall, she is lovley and can tell you what else they have on there.
Swimming - Tadley pool has a floor that comes up so is only an inch or so of water of one end then gets deeper so the children can walk in. They have jelly babies sessions, on tuesday, thursday and sunday - not sure of times, phone to check.
The sports centre in Fesitval Place has swimming pools and lessions which I gather are good. Every day they have sessions in their indoor soft play called Gym Tots, not sure of times, different according to age of child. Go in and ask them what they have on.
The NCT is very active in Basingstoke and you don't have to be a member to join in activities or coffee mornings. There's coffee mornings in Chineham or the ones in Old Basing on a wednesday morning are popular - you'd be made very welcome.
Good Luck.
I like living here - hope you do to. x