Hello! I went to Portugal alone 2 years ago (I'm 23 now) and it was fabulous. Down in the Algarve are some really nice beaches, and I stayed with a family for a couple of nights that I met in town (would only recommend this if you feel comfortable, and have a good grasp of who to trust). Think Lagos area.
Most of Portugal I found to be very friendly and welcoming as a solo traveler. Lisbon is an amazing city and I stayed at the Lazy Crow Hostel which I liked very much. There are a few neighborhoods to avoid when alone, but the main part of the city is fine. There are tons of things to do in Lisbon! I was there a week and felt like I could still look around. People were easy to meet.
I also visited Porto, Sintra, and Coimbra. Coimbra is a college town and has a lot of young people, but my experience was not that great. It does however have lots of little shops to look around in and some very tasty pizza. Sintra is a nice place to go as a day trip from Lisbon. It has a large castle with Moorish origins. Porto I liked because I love Port wine, and there is plenty to be tasted if you are interested.
I heard the Douro Valley is very pretty, but I did not make it there.
Last things: use the bus and public transportation. Its helpful and goes most everywhere. And please, if you go to Porto, don't stay in the HI youth hostel. Its way too far from the city center.
M