Nord verso Bologna Template:European Route Number
Untested, but the other side of the autogrill listed for going south should have plenty of traffic going north past Firenze.
Altra opzione: Fedcas took the train from Firenze to Pratignone (eur 1,90, about 20 min), then it's a 5 min walk to the A1 highway (see the spot on the map, Pratignone is N-W from Florence, where A1 crosses A11). It's a big commercial area so there are lot of trucks during the working days.
Yet another option: take a bus from the train station (Santa Maria Novella) to the airport, where the A11 highway starts. (The best option is to take the bus that goes to the airport, as there are many busy intersecting highways in the area that are difficult to cross if you don't get dropped off in the right place.) There is a petrol station on via Vialle Alessandro Guidoni, near where the highway starts.
South towards Rome, Napoli Template:European Route Number
Guaka and amylin were dropped at a good motorway entry south from Firenze. You might be able to get here with bus no 36 or 37. You can stand underneath a bridge, way before the usual big sign saying "No autostop".
There is a great autogrill on the A1 south-east of the city near the town of Antella, lots of cars and trucks going south. Take bus 31 or 32 from 'Piazza San Marco' to the last stop in Antella. From here you can walk about a kilometre or take bus 24 to 'Peruzzi 04.' You can see the autogrill from the 'Peruzzi 04' stop. There is a fence, but the gate was unlocked. If you choose to walk then just stay on the main road that goes through the north part of town along the A1 until you get to the autogrill (just follow the 24 route). The road doesn't have a side walk, but there isn't much traffic. You'll go up a hill as you exit the town, the autogrill is at the top of the hill. If you want to go north there is also an autogrill on the other side of the A1 here. There is a road that takes you under the A1 to the other side. Trewge found a ride to Rome almost instantly.
Another option: see "going North" paragraph
When hitchhiking to Pisa, try to go by motorway Firenze-Mare, which you can reach by going to the airport. Don't go by the federal road, there are no petrol stations and lots of "No autostop" signs.
From the train station Santa Maria Novela, get on the tram line T1 in the direction of "Villa Costanza" (you can't go in the wrong direction anyway, the train station is the beginning/end of the line). Get out at "Talenti" stop (just before the tram goes underground). Go on your left (when going out of the tram) and reach the roundabout. There starts the highway to Pisa-Livorno called "Viale Etruria" at this point (becoming SGC Firenze-Pisa-Livorno a few hundreds meters away). You can try to hitch hike from the roundabout or try at the petrol station further on the road, about 15 minutes by foot from the roundabout where you will catch more traffic.
(I waited about one hour at the entrance of the gas station, trying to stop cars. Finally decided to go towards people at the petrol station and got a direct lift to France after 5 minutes. Since vehicles are approaching quickly at the petrol station, I would recommend either asking people at the petrol station or standing at the roundabout next to "Talenti" because it seems hard to be able to stop cars coming at rather high speed with no intention of stopping for petrol). (Anne-laure June 2013)
Parco di Rusciano (Southern side of river Arno, 20 min walk from city-centre) is a very nice place to pitch camp. Very quite area. Only one entrance to the park (or two, not sure). Very nice green grass to crash on, olive trees to set a hammock, salvage mint to make herb teas and laurel tree for cooking experiments. But it seems that Firenze is nicely surrounded by green areas, so you should be able to find other great spots somewhere else.
If you have European ID, you can register for free at the "Biblioteca Nazionale Centrale di Firenze" (and probably in other libraries) and you have unlimited time access to a computer with Internet. It's open from 8.15 to 19:00 from Monday to Friday and from 8.15 to 13.30 on Saturdays. Otherwise there are a lot a "Internet Points" in the centre, where it is eur 1 per hour (you can't ask for less than an hour), and they are open later at night and on Sundays.