Are there any mountaineering/hiking activities in or near Albufeira, Portugal?

I'm heading over to Albufeira, Portugal on Thursday and I was just wondering if there are any hiking or mountaineering activities, or outdoor landmarks worth seeing in the area (or close by).

I don't want to be stuck on the beach with my friends the whole holiday, and from what I can see on TripAdvisor it's just beaches/typical tourist stuff.

Anyone know of any, through resources/personal experiences local to there?

Note:

• I would define local as probably within 25 miles of Albufeira.
• I haven't been to Portugal previously, so I'm unaware of any of the surrounding areas. (I'll be going off Google Maps or a real map of some kind only)