Pisa and Florence are the closest airports to Lucca - Pisa is about 30 mins away and Florence is about a 45 min drive (90 min by train).
Milan to Lucca is a 3.5 hour train. Rome to Lucca is a 3.15 min hour train. You can also get a connecting flight from these major airports to Florence or Pisa.
You can bus, train or drive from Lucca to Florence, both are around an hour away.
Viareggio is the closest beach, Forte dei Marmi is also a beautiful and very popular destination along the coast. Cinque Terre is about 1.5 hours by car, 2.15 hours by train.
Staying within Lucca's historic city center will be most convenient. The city is super charming and very walkable and it will also be easier to reach the main train and bus station from this part of town. If you are renting a car, then you obviously have more flexibility and may choose to stay in the Tuscan countryside outside of the city.
Lucca's city center is approx 15 mins from Villa Grabau. You can easily take a taxi to the villa and we will arrange for a taxi company to take people home at the end of the wedding back to Lucca.