The main decision is whether you do a 'self guided' visit using public transport and your own research or book a tour through one of the many companies. Day trips you can do yourself from Florence include:
SIENA : One hour on the bus (less than 10 Euros). Frequent buses (2 per hour I think). Florence centre to Siena center. Just remember the last buses don't run all that late (8 or 9pm)
PISA : Bus or train both take an hour or so. Very cheap (again less than 10 euros). No tour required!
LUCCA : Train. Arrives right outside the city walls of Lucca. Takes under an hour and well worth a visit.
AREZZO : Train. About an hour
Hilltowns (Montalcino, Montepulciano, Pienza etc). By the very nature, perched atop hills, they are inaccessible by train. Bus services are few and far between, and though possible from Siena you will find yourself spending large parts of the day waiting on connections. Best have a car/driver or take a guided tour.
Vineyards/Wineries/Wine tasting: Almost always inaccessible by public transport, by being located in the countryside and often on hillsides, these are best visited by taking a small group tour. Italian drink driving laws are even more strict than in the UK/US so a self drive exploration of the wine regions, nice as the idea may seem, is pretty inadvisable.
Definitely look in to doing things yourself wherever possible. You can not only save some money but have much more of an adventure. Italy must be one of the safest countries in the world to visit as long as you are sensible.
I looked into doing a tour with Artviva but it seemed like quite a big operator and decided to go with a smaller company called Slow Days. They have reviews on Tripadvisor - here. or google Slow Days Florence for their website
Remember that August in Tuscany can get really hot - good idea to have at least one day out of the city!