You could contact this lady for play dates. She organises activities for mums and little ones. Send her a PM and she'll give you more details. Neuchatel English Play group
There's the Neuchatel international club too but if you contact the lady above ( via PM) she'll give you all the details of that too as she helps with the kids activities there too.
There is La Courte Echelle which is a popular meet up place for mums and kids.
As Odile says where you live will probably depend on where your husband is working but actually nowhere is very far in Neuchatel and most places are easily accessible by public transport.
The nicest family friendly areas IMO would be Marin, St Blaise, Hauterive, and the villages like Cornaux,Cressier, Thielle, Le Landron etc going north or Boudry, Cortaillod, Colombier, Auvernier etc going south.
The former are generally speaking cheaper than the latter both in rents and taxes.
Welcome ( soon) to Neuchatel.
Happy to meet up for coffee and show you around when you get here or if you come to visit beforehand.