You can do trekking. Half hiking half mountain climbing- start at the picnic area just outside and hike to the lagoon nested in the mountain range(the aformentioned 'Circus' Miguelito mentioned- its called that because of the lagoon and other pools around it). There is a refuge there- but is often full- you'll see people camping just outside (like we did) no its not really permitted, but the guardia civil will come and warn you to pick up your tent before giving you a ticket. Just ask the other campers when they get there if they've come or not, they usually only go every couple of days. The next morning- refreshed from a nights sleep (careful, there are wild horses that come to the lagoon to drink at night, but they won't bother you- and sheep and mountain goats!
) climb your way to the sumit! VERY cool, very worth the trek! While you're heading to the top you can leave your pack at the refuge. Then continue all the way back to the picnic area the next day. Its hard to recall, but I think it was 15Km? round trip.
ALso, there is what is called Nieve perpetua- Perpetual Snow! In the summer its not much, but you still see it. Very cool. (when I went it was a rather large patch, but just a patch, still it was neat knowing there's always SOME of it there year round.) ALso, don't bathe inthe lagoon... @ people from my group did, but they didn't warn us until later, they were fine... but apparently its not recommended because its sedintary water- so it could have all sorts of bacterias and extra friends you wouldn't want to pick up! :p