"Hostal" and "Hostel" are equivalent words, according to the Spanish Tourist Office. I equate them as well. Do you mean "Hostal" and "Youth-Hostel"??
I invite you to utilize the SEARCH link above/right and type HOSTAL BARCELONA as your keywords and you'll likely find dozens of previously posted threads suggesting many many places where people have stayed and enjoyed.
If you're looking for a youth-hostel,
Kabul Youth Hostel is world famous and is also known as a "Party Youth Hostel" so keep that in mind.
Not sure about Valencia myself, but you might try the SEARCH feature for that as well. And you're leaving March 7th?? Wow! You'd better make your reservations soon!
Saludos, MadridMan
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