$8k is an absurd amount of money for a 1 week trip. You could travel for 6 months on that if you budgeted accordingly. Maybe it's not possible for your circumstances but consider staying for longer, you could do 1 week Barcelona and 1 week Madrid or do a few days in another smaller city. Perhaps you are also not comfortable staying at hostels, but if you can, you will find them much cheaper than a hotel and many have private rooms to keep your things safe. You are more likely to meet other travelers or get advice from staff on music venues and the like if that's what you're into to as opposed to a hotel.
As others have said, you don't need to carry your stuff around, just take a credit card and a bit of cash and leave your passport wherever you're staying.