Welcome to Basel, it is a great place to have kids, but a lot better when the weather warms up and we can all get out to the parks again!
Try the BCT, Basel Childbirth Trust, they have various playgroups through the week. Beyond Bruises is probably the one for you on Friday afternoons. It is a fun meeting place with other English speakers and fun things for the kids to do. Check out the website for more details.
http://www.baselchildbirthtrust.com/
The BCT is also a great source of information on ex-pat family life and a good social network too.
Swimming lessons- try at a local pool and see if you can pick up a leaflet as there are usually lots of swimming lessons, and the language doesn't seem to be much of a barrier in the water.
Check at your local Gemeinde for details of Waldspielgruppe, forest playgroups where the children go off to the forest and grill sausages etc for the afternoon (if you can get over the health and safety aspects!).
That's all I can think of for now,
Have fun,
Hazel