What is the best beach and bagni for a day trip from Lucca?
Yep. Viareggio is where the Luccans go. Ask the people where you'll be staying for specific recommendations. But if it's the offseason, Viareggio pretty much rolls up the sidewalks.
Viareggio is probably the best beach for a day trip. We were in Lucca on May 1 and the trains were standing room only (if you could get on) heading to Viareggio. I don't know about the best bagni but there are a couple in Bagni di Lucca.