I hated beach holidays and I never had a holiday lounging by a pool before kids but now... I will only consider a holiday where both kids are going to be entertained so beach holidays are at the top of my list! And lounging about is bliss with small children - we keep everything very low key as just a holiday house with access to a pool is endlessly thrilling for a small child!
We usually self-cater on a bigger site somewhere - must have aircon if it is somewhere hot - so we have room for the kids to play and a separate room to sleep in and a proper place to cook (keeps down cost, we can eat when we like and make picnics, and helps feed our fussy kids). And we hire a small car so we can day trip or stock up at the supermarket or local market.
You might look for somewhere with a kids splasg pool, some interesting local scenery or museums or towns where the kids can scamper about, weather that won't roast little one (so in high season rule out Greece, Turkey, and a lot of the southern European hot spots).
Increasingly as we think about the impact of travel on global warming and our kids' futures, we stay in the UK or northern Europe. We had an amazing week at the Dutch Centreparc at Port Zelande on the widest, cleanest beaches you can imagine, combined with a few days stay at Rotterdam where we did the food hall, the maritime museum, a day in Plaaswijkpark which was SO cheap and fantastic. In Rotterdam we parked the car up and took buses and trams everywhere which our DD enjoyed.
We also enjoyed the Village Nature centreparc just outside Disneyland in Paris.
I would recommend Jersey in the channel Islands too - the beaches are beautiful, the Gerald Durrell zoo is a perfect day out, and the weather is typically lovely. A hire car is handy although the roads can be a little bit hair-raising!