Perfectly fine for children.
Of course places like Playa D'en Bossa and San Antonio are more the party areas but there are hundreds of places on the island which are beautiful and very relaxing places to be, the North side in particular Portinatx.
Don't be fooled though the clubbing season starts from early May over there not June but I wouldnt let that put you off. Some areas I would recommend that aren't the party party places would be Cala Llonga (and anywhere up the coast from there so Santa Eulalia, Es Canar, Cala San Vincent), Portintax and Santa Agnes and Sant Miguel. There will be a lot of child friendly hotels and resorts in Cala Llonga/Santa Eulalia area.
Ibiza Town is worth a shout too but there will be more nightlife there but the town itself is beautiful and again, perfectly fine for children, and to be honest San Antonio itself isn't that bad if you stay out of the West End mainly. Have seen plenty of families with kids on the front where Mambo's and Cafe Del Mar is.