Are there any towns/cities that we should plan to spend more than one night at?
Dingle Peninsula without a doubt. Sleep in the town of Dingle, one day touring the peninsula and one day touring the town.
Marsha, depending on your time available, you might want to try to spend at least a couple of nights in each place. We have found as a rule it is preferable to forgo seeing some things in order to spend a couple of nights in order to better appreciate those places you visit.
I'm with Ron, try staying in say 4 places, North, South, West and Dublin. Those are good jumping off points to check the area without moving around too much. You may find a place you think is great or you may learn you don't need to stay there NEXT time, but at least you are getting to know the area and a host if B & B's are your style. We still love our landlady from Malahide north of Dublin; unfortuantely she isn't doing the business anymore ;-(
therein lies the challenge in Ireland. It takes a bit of driving to get from one spot to the other. Spending one day anywhere is not worth it. 2 days at least.