On the Adriatic side, the coasts of Emilia Romagna and Marche are probably the most commercial. The Conero coast is lovely and there are some great bits of Marche further inland if you want some mountain scenery to get away from the heat. Bit further down there are some nice stretches in Abruzzo, a region which has some great food and drink and some spectacular mountain scenery in land. Puglia is probably your best bet, some stunning stretches of coastline, great food drink, wonderful people and well-enough organised for families.
On the west coast, Liguria is very beautiful and Genoa is a great city. The Tuscan coast has some nice spots, the Costa D'Argento near Grosseto is really beautiful. Lazio and Campania are better known, especially if you have been to Sorrento before. Calabria is one of my favourite regions in Italy but not sure it's great for a family beach holiday. Sicily is stunning, one of the most amazing places in the World I think. West coast is incredible in parts. The area south of Messina is a bit more built up but has some beautiful places to see including Etna and could be a good bet. Sardinia I don't know so well but seems to be a good mix of gorgeous coastline and organised tourist areas.
To cut a long story short, Veneto and Emilia Romagna may be your best bet for a well-organised, family package type place with some sites to see, but will be packed. Puglia a good option I think.
