Hi there and welcome to Basel.
Are you looking to live in an ex-pat area? The biggest areas are Storchenweg neighbourhood in Oberwil and in Reinach behind the International School. Both are very family friendly areas with lots of families in a similar situation with young children. However you do pay over the odd's for living in English speaking surroundings and it can be harder to integrate into the local Swiss community. It depends if you think you will be going down the ISB route for your children or local kindergarten. It might be worth checking availability. Any relocation agency would know of any apartments/houses which are available in these areas.
Also for just getting out and about have you found out about the BCT- Basel Children's Trust. They have lots of playgroups for children, information about schooling and much more.
www.baselchildrenstrust.ch.
I hope you are enjoying Basel so far, I've got a 6 year old and a 3 year old (and an imminent bump) and we've somehow been here for 4 years now and love it. Basel is a great place for families.
Take care
Hazel