Lecce is a city in southern Italy. Very nice to visit the historical centre, also its people are very warm and hostful. university city as well.
You will have to take the S.s. 613 road. It is a high speed road so you won't have other access soon and it will be forbidden hitching on it. The best spot is very close to the bus terminal, so lots of local/city buses bring you there, you just ask for "stazione dei bus" any person can tell you which number. From there you can start hitching from the roundabout (Fedecicco was asked for a lift without either pointing my thumb out, just seeing backpack) but better to go a bit further there will be 2 petrol stations (in Italy hitching outside of petrol station is very hard).
Sleep and accomodation
There is a good Couchsurfing community, you may easily find a host. If not just go to the sea, San Cataldo or San Foca, very close. Very crowded in summer.,but also very nice.