North//West towards Coimbra, Lagos, Albufeira, Lisbon, Porto
Walk towards the main train station and then just follow the road towards the Jumbo Shopping mall. From Faro city center to this mall it is a walk of 1.4 km or less. Cross the Jumbo Mall in the direction of the airport and then there is a petrol station that you can hitchhike from to Albufeira and Lagos, which also have the highway toll and national road going through them all the way north.
Make sure you get a ride with someone who is ready to drop you at the highway petrol station or a good point on the national road towards Lisbon. While heading to Lisbon which is fairly easy, if you are able to get to a petrol station or a good spot on the national road in the direction of Lisbon, be patient and wait for a ride with someone who is going all the way to Lisbon. If you are impatient and accept a lift from just anyone, you may end up stuck in small towns or isolated spots which are difficult to get out of.