>>1926547I highly recommend you to go to ordesa valley and then to "monte perdido" or "la faja de las flores" (you can climb it, but there's not need to, you can just hike it, its not much crowded and its one of the most beautiful places i've been, pic related). Other recommendation could be Pineta valley and La Real valley (you can go to this one hiking through Pineta).
Just take a look to this three valleys and the trails and peaks you can hike from them and to "la faja de las flores", there are lots of mountain huts in all of these places in wich you can sleep for free (unless you go to ordesa, then you need to pay for sleeping, have a tent or do what I do and sleep in a cave near the mountain hut)