Hostal in Spain does not mean youth hostel although they do have them. Often a hostal is simply a small family run B&B which is what you requested. $100 is only 77€.

While the Four Points is a good price, I prefer staying more central.

Madrid Man has a long list of Barcelona hotels/hostals.
http://www.madridman.com/barcelonalodging.html

From Madridman's website:

WHAT is a hostel/hostal? Hostels, called "hostales" in Spanish and "hostals" in Catalán, are usually very quaint (small), family owned and operated hotels and can be found in some of the most historical, interesting, and active parts of the city at very good prices. Hostels in Spain should not be confused with Youth-Hostels which are called "albergues juveniles" in Spanish.

We are staying at the Marina View Bed and Breakfast in May. The staff has been great and it had very good reviews on Trip Advisor.