Cabo da Roca
Cabo da Roca is the westernmost point in continental Europe, located in Portugal close to Lisbon. There isn't much to do but it's a beautiful place in a special location which makes it a great starting / ending point for an epic hitchhiking adventure!
Hitchhiking out
Finding a direct lift back to Lisbon is definitely possible. If your driver doesn't go to Lisbon directly or you want to go somewhere else further away, it would be advisable to ask your driver to drive you back towards Sintra.
Hitchhiking in
If you come from Lisbon, best is probably to hitch to Sintra first. Further instructions for that are on the Lisbon article. Once in Sintra, go to the big roundabout next to the art museum and try hitching at the bus stop west on the N247 road. There might be lots of other pedestrians and generally chaotic traffic though, so it might be worth it to walk for a few minutes on the road west until the next bus stop. Otherwise, hitching the N247 until Cabo da Roca is fairly easy and very straightforward, lots of slow traffic and both tourists and locals are very friendly. You probably need multiple rides since most cars are just going to the surrounding villages. Perhaps if you tell your driver about your interesting journey to Cabo da Roca they might be nice and drive you all the way.
Sleep
There is lots of nature and beautiful beaches, especially around the hiking trails going north. Wild camping there is definitely illegal but some people do it anyway, just be a little bit cautious and it should be doable.