Beach/coastal towns in Italy

What are your favorite beach towns in either Puglia or Sicily? I'm looking for a beach that's not too crowded (umbrellas taking up every inch of sand - I'll be there in early June) and a town that feels somewhat authentic, i.e. not too touristy, and has lots of good restaurants. Bonus if it's easy to get there by train or bus. Thanks!

Edited: 16 May 2018, 05:58