I'm looking at going to Sicily at Easter and there is lots to do there (even a real live volcano!). Around Taormina is meant to be nice (though I am not talking from personal experience... only from browsing websites). Lovely sea and you can still get to Etna from there and even possibly a day-trip to Palermo.
If you want more 'culture' in Italy then I would recommend Tuscany. You could stay in the countryside, but visit Florence (to be avoided in July/August - it's hotter than hell and there are no Florentines there, only tourists - but fab the rest of the year) and also Siena (gorgeous), Pisa (leaning tower bound to be a hit with any 5-y-o, surely?), etc. If you want a beach, you can stay on the coast near Pisa. Haven't stayed there, but Castiglione della Pescaia is a lovely place.
I also like the North-East. Had a nice (but very quiet - no-one there!) holiday in Friuli last Easter. But if you want more going on, you could stay within reach of Venice (I wouldn't say in Venice as it's so expensive) somewhere where there are other things to do... I like the area around Bassano del Grappa, for example. Lake Garda is also gorgeous. And you could easily work in a day-trip to Venice from either of those. Not on a beach though. Places like Lido di Jesolo seem a bit built-up and touristy to me, though again I haven't actually stayed there, so might be doing them a disservice.
My final suggestion would be the southern tip of Puglia. Haven't been there since I was a student, but very beautiful. Very uncrowded. Also very beautiful old towns, like Gallipoli.
Have fun. Sounds like you all deserve a break.