We stayed at Hotel Palace, just across the street from the beach, because we got a great deal there -- end of season rates (late September). It was very nice, but seemed more of a business hotel than a typical Italian tourist hotel. It even had elevators. Our room was great, with a balcony overlooking the sea.
With kids, though, I would probably look at one of the many hotels right along the beach. Many of them have private play areas right on the sand. Check Trip Advisor or Booking.com. If you can find a hotel that is fairly close to the train station (even if you have a car) you will ensure that you are in a pretty central, walkable location.
If you should have a cool or rainy day, I recommend that you go downtown and find a cafe called La Meridiana. We had the most amazing hot chocolate there, each cup served with a little plate of cookies and a bowl of whipped cream.