I am traveling to Segovia for one night in April with my son. Does anyone have a recommendation for hostals in this city? Many of the hotels are already booked for April 14.

Have you conducted a SEARCH using keywords SEGOVIA HOSTAL? You might find some recommendations.

There are two hostels (called "hostales" in Spain/Spanish - not to be confused with YOUTH Hostels, though, which are called "albergues juveniles". The word "hostals" is actually Spanglish and doesn't exist except in Catalán, the regional language of Cataluña) in Segovia which have websites. Here they are:

Hostal Don Jaime
http://www.viasegovia.com/hostaldonjaime/index.htm
Located within 100 meters and in sight of the aquaduct in a rehabilitated 19th century building. Rooms have bathroom, TV, phone. Breakfast in dining room available. Reservations by phone/fax. No prices listed. Website in Spanish.

Hostal Plaza
http://www.hostal-plaza.com/
Located 50m from Segovia's Plaza Mayor. 17 rooms all have bathroom, TV, phone, & air conditioning. Seasonal prices. Reservations by phone/email. Credit cards accepted. Website in Spanish. Bar-cafteria onsite.

Good luck and enjoy your time in Spain! Saludos, MadridMan