Florence is perfect as a base from which to visit Tuscany
First off, I have to correct the information you were given above which is in part incorrect and in part outdated. Buses within Florence are an excellent way to get around town, especially if you're trying to get from one place to the next quicker than you'd get there on foot. The bus system in Florence is run by
ATAF (and not by SITA, those are for outside Florence) and you'll find stops all over the city although the SMN train station does act as a hub for the majority of the lines.
You can take bus #7 to Fiesole for a wonderful day trip to see Florence from above, as well as visti the Etruscan and Roman archeological remains in what was once the first habitated center in the area, before Florence. Another wonderful panoramic view of Florence can be seen from Piazzale Michelangelo - you can get there by catching the ATAF #13A either on Corso dei Tintori near the corner with Via de' Benci or on Lungarno Serristori right after the bridge called Ponte alle Grazie (
stops 17 and 18 on this map)
The smaller electric buses that pass through the historical center are no longer called routes A, B or C but C1, C2, C3 and D. You can
see the routes here.
For ideas on what to see, take a look at
this itinerary of Florence in 2 days - you can definitely do it over more than just two days, taking it a much more leisurely pace to better enjoy each site.
Florence will be an ideal base from which to see both Florence and the Tuscan countryside. You can do day trips using trains to move around - highly recommend a day trip to Lucca and Pisa and Arezzo. You can do another day trip to
Siena, a medieval town highly recommended, but to get there I recommend the
SITA bus instead of the train that also leaves from the SMN train station. It is direct to Siena with no need for changing trains and drops you off closer to the main sights.
As for
Venice, it is further away but you can still manage it with the one overnight as you're thinking. Take the train (the fast train gets there is about 3 hours) and return the following day on another fast train. It definitely is enough although in late June you'll find Venice really crowded (most towns will be crowded but there is limited space on Venice since it is an island so you really notice it there). If you are on a budget, I would skip Venice at this time - because it is high tourist season, everything will be at its most expensive in a town that is not known for being affordable.
If you have any further questions, let us know!!