I'm not familiar with any "hostals" (as they're called, in plural, in Catalán or "hostels" in English) which have kitchenettes or access to any onsite kitchen facilities.
You will find this, however, in youth-hostels in Barcelona but I'm not sure you're willing to share sleeping-space with a group of (snoring) strangers or not. If not, you may have to "spring" for a kind of vacation apartment but these are typically much more expensive, probably cost prohibitive when comparing the price of this with the lower price of a hostel + eating out. Just depends on where you want to spend your money.
Best of luck! Saludos, MadridMan
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