I coundn't find any that less than $100. dollars
if you cannot find your personal "Prince" incl. "castle" to stay...
you can visit all over Europe
They have low budget chains like
ETAP / FORMULE 1 and you get in Barcelona double rooms from 32,00 EUR (less than 40,00 USD).
(Functional, clean and a lot of self-service - reminds more to self-storage units incl. beds - but for those who need only a bed and stay the whole day outside. It's no "spa" to stay the whole day inside!!! Maybe perfect who need a "locker" incl. "dressing room".)
Their low-mid budget chain calls IBIS.
Their high-mid budget chains call NOVOTEL and MERCURE.
Further recommendation to find a hotel under 100 USD in Barcelona:
Hotel Reservation System
the Spanish hotel chain NH Hoteles
Good Luck and have a nice travel!