It's half the distance from the Grand Hotel Royal to Piazza Mazzini, which is the terminus of the local inter-city bus routes. Seven hundred meters down Viale Carducci, or about 8 minutes on foot (heading SOUTH).
You can get to Lucca, Florence, Pietrasanta, Camaiore, Lido di Camaiore, Marina di Pietrasanta, Forte dei Marmi, Pisa, and elsewhere by bus. It's a useful alternative to taking the trains from the more distant train station. The last part of the walk to the train station (inland from the Lungomare) is somewhat dreary.
I would take the nonstop bus between Viareggio and Florence, instead of the train. It's faster and more comfortable. Tickets (sold according to distance) are sold in many tobbaconists, bars, and newsstands, as well as at Piazza Mazzini.
Buses going north toward Forte dei Marmi even stop nearly in front of the hotel. At Forte dei Marmi, you can connect to another local bus continuing north to Marina di Massa and Marina di Carrara.
Here are the bus schedules:
When consulting the bus schedules, pay close attention to the DAYS of operation, as schedules are usually different on Sundays and sometimes on Saturdays as well.
Edited: 2:46 pm, May 06, 2012