We did the Best of Tuscany tour a month ago; yes, Florence was very crowded. The guides we had were very helpful with that, but definitely be prepared to be on the streets with lots of tourists.
Having said that though, it was really nice at sundown; I remember walking back from a restaurant in Florence at about 6pm, and the streets were really nice. If you want to have a truly spectacular Tuscan meal, which will be a couple of blocks from your Florence hotel, check out Cafaggi; your guide will probably walk you past it. We had our best meal there--highly recommended.
When the tour ended in Lucca, we took a train to the Cinque Terre--I don't think I would recommend that. It was super-crowded, and not what we were expecting. The train was easy though, and if you don't end up with a car, the train is simple to navigate and very reasonable.
Most of the places you'll go are off the beaten path; Siena is the only other decent-sized city you'll visit, and it wasn't bad at all; Volterra is a tourist site and was very busy, but still not so bad, and we enjoyed it.
Our tour went to Elba; it was very nice, but rain kept us off the beach. We walked through the small town square after dinner one night--not a big place, not sure whether I'd say it's worth a day, but there weren't a lot of tourists and it was easy to navigate.
You'd almost certainly need a car if you wanted to stay in the Tuscan hills; there's just not much out there, and driving would be a pleasure anyway--the countryside is truly beautiful. I'm not one who would want to drive in the UK, but I'd gladly drive in Tuscany; traffic is light, the roads are pleasant, drivers aren't crazy like they are here in the US.
Our favorite spot, and I'm guessing your tour willl go there, is Gargonza; wow, what a great place to stay--I'll say no more and let you be pleasantly surprised!
If you have a car, you'd probably enjoy any of the many small towns that dot the Tuscan countryside; your tour will bypass Pisa, which is apparently super-crowded--not sure it would be on my list if I were returning. We talked about how much fun it would be to find a small quiet village and spend the day there; they're all over, and could make for a great relaxed day.
If we were to do the tour again, we'd probably spend a few days in Rome, which is always worth a return visit. Having been there before, we'd skip some of the main draws (the Colosseum, the Vatican, and the Pantheon), but there are so many other places that are incredible and well worth a visit. For example, consider going to see the Baths of Caracalla, which we toured and which were almost completely empty, and which were fascinating. We'd also love to see the Appian Way, which we didn't get to see when we were there last year.