There are several possibilities to go for a swim:
– at the beach: e.g. in Castiglioncello, just south of Livorno, a picturesque rocky coastline with sandy bays
– to Lago Braccini: close to Pontedera, a sandy beach with parasols and deckchairs, and a bar-restaurant Amalia Laghi (Via delle Prunacce, Pontedera)
– to Castelfalfi Resort: luxurious pools, beautifully situated in the hills
– to a Municipal Swimming Pool: almost every somewhat larger place has a communal pool, e.g. there is a nice one in Peccioli (Google: Peccioli Municipal Pool)