The Hague has a nice youth hostel located in the city. Trams 1 and 16 stop very close and all go to the Convention Center.
The hostel, a historic building, has been completely renovated and the interior re-designed as a youth hostel with all modern facilities. There are 220 beds in total, in 2-, 4-, 5- and 8-bed rooms with showers and separate toilets.
For your bookings please go to: http://www.stayokay.com/en/hostel/den-haag