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Go where the A44 crosses the A329 (location on map), and get on the A329 towards the A92. This is the motorway between Sevilla and Granada.
Take the bus SN3 or SN4 and get out at Faculty of Fine Arts. (Facultad de Bellas Artes) From there, continue walking straight on in the same direction for about 15 minutes and you'll get to a petrol station Repsol. The traffic is low and it's 8 km before the highway. Try to get a ride after Santa Fe.
A good place to start is Granada's service station ("via de servicio") in the north of the city (that's where most of the people heading north enter the motorway anyway): Where "Carretera de Jaen" (also called "Av de Juan Pablo II"?) and the A44 meet, you find a big roundabout below the motorway. Take the exit "via de servicio" (or if that exit doesn't exist, then "poligono indistrial" - sorry, not sure!) There's a petrol station where you can find a ride. Have in mind that most of the drivers there will go to Jaen.
Get any of the entrances next to the A44 and use the direction of Lorca/ Guadix (A92 and later A91). Best thing would be to wait for someone who actually is going into that direction since the A44 crosses the A92 after 5-10 minutes. You can as well hitch directly on entry to A92. If you get a lift going only to Guadix, you can leave on a gas station just before Guadix. From there you can ask for lifts towards Baza, Lorca, Murcia. There is not much traffic there so even lift to Baza might be worth of taking. One of the next places you can get to is Puerto Lumbreras where is the highway spliting. If your driver goes to the coast you can get droped on a gas station in Puerto Lumbreras. The station is out of highway so there is a lot of local traffic but you should be able to get lift to Lorca from where you can hitchhike on one of the junctions lift to Murcia. The fastest option could be to leave on a Repsol gas station shortly after Librilla. It is the only gas station between Lorca and Murcia which is directly on the highway. On highways in south spain there are many gas stations which are out of the highways and even though they are next to the highway near to the junctions they are usualy very empty and the few cars who come there are local so you should stick always to the gas stations which are directly on the highway. From the gas station in Librilla you can hitch a lift with everyone going over Murcia in direction Elche/Alicante/Valencia. Shortly after Murcia near to town Santomera there is a nice Repsol gas station. If your driver doesn´ t go further then Elche or Alicante you should leave here and search idealy direct lift to Valencia. There are two diferent highways between Murcia and Valencia. One option is A31 from which you turn on A33 and A35. A31, A33 and A35 are autovias which means they are free so probably more drivers go this way. If you would get a lift just part of the way it will be dificult to find a good spot to hitchhike. First good station would be after la Font de Figuera. It is recomendable to wait for a lift which takes you at least there. Other option from Murcia to Valencia is to go via Alicante and then by AP7 to Valencia. On AP7 drivers need to pay toll so there is not that many cars ussually. There is a gas station between Elche and Alicante from where you could search lift to Ap7 on which there are then couple of gas stations. It is recomended to searcch lift from Santomera directly to Valencia as if you take shorter lift it is likely to get stuck somewhere. If you are on A35 and your driver goes to only Valencia and you go further north you can leave on a gas station after Alberic and Massalaves. From there you can search lift going to Sagunto or further north. IF you are on AP7 you might as well want to leave on some gas station and search lift to Sagunto. there is as well a gas station on a highway ring around Valencia which might be also good place to change cars but you should make sure that your driver is really going by this station. If you get over Valencia to Gas station shortly before Sagunto you succesfully managed to get from south spain and now it is easy. From Sagunto until Barcelona there are couple of good gas stations and it should be fairly easy to get to Barcelona. If you go towards France leave on gas station Porta de Barcelona which is positioned just few kilometres before Barcelona and is a good spot for searching lift to Girona or France. Leaving from south Spain is usually quite time taking so for the way from Granada to Barcelona you can count about 3 days on the highways. Try to never get to small gas stations out of highway.
Take the metro to the last stop "Albolote", then walk north towards the highway (ca. 2-3 km). There is a gas station on the left handside of the bridge over the highway. It is a really good spot. Direction Sevilla there is one more of the good petrol stations, right after Lorca.
Direction Málaga via Santa Fé
We walked all the way from Granada to the first petrol station in Santa Fé, which is definitely not recommandable (but doable in a way).
From the end of Granada you can hitchhike a car to Santa Fé.
In Santa Fé you should check really hot springs!! - No. The hot springs are closed!
Granada (map) has a national motorway called A44 just around the city. There are many exits on this motorway. When you are on the A44, wait for exits with direction city center. The driver can easily get off and on the A44, in either direction.
Just after the district Albaicin or after cemetery there is mountains where you can find good places for a tent. It's about 30 minutes on foot from the city center. Locals who live there do not care so much about tourists with a tents. Also in this hills there are some caves where people live. Maybe you'll be lucky to find any empty cave for your own or someone invite you.
Church serves a free food and offers a free shovers