Try Cattolica, which is near Rimini, on the Adriatic coast. Yes it has a beach, but these are very well organised. Most of the beach is privately owned and you pay for the use of a sunbed, but the facilities are brilliant. Most of them have a childrens play area, games (table tennis, boules, table football), toilets, changing rooms and showers, a pool and a jacuzzi, the one we used last year even had a gym. They are very, very clean, and there are boat trips you can take. There's a local coach company which does day trips (we went on a couple - one to San Marino), and a railway station, so you can get out and about if you want, though we were happy to spend time there. There's an aquarium in Cattolica which apparently is very good. I would suggest that you go half board. We had a buffet breakfast every morning and there was a choice of meals in the evening. Many of the hotels have pools, but we preferred the beach. Italy is very child friendly and I'm sure you'd have a great time.