I would recommend you go with Lahinch. It's a town with some nice pubs,shops and a great beach (if you get the weather). But it's still fun to watch the surfing on a windy day :-) Doolin is really only a small village with a few pubs, a shop and mostly now made up of holiday accomodation.
If you base yourself in Lahinch, you can easily drive to Doolin to visit and also take a boat trip to Inisheere.
You can also take a spin to Ennistymon where there is a nice pizza restaurant called Holywell. Nice treat for the children.
http://www.holywell.net/restaurant/italian_ennistymon.asp
If the weather turns nasty you have a swimming pool and aquarium in Lahinch also :-)
http://www.lahinchseaworld.com/