Hi barenakedcakes (great name btw
) ! I stayed in Eger 3 years ago, and the most affordable place for overnight was the "Tourist Motel", at the opposite of the city from the station but close to the castle. Maybe a 20-minute walk. At that time, it was around 15 euros with shared bathrooms. Clean rooms, and friendly staff. But I was there in April. During the summer, colleges offer their beds at a very low fare (4 Euros or so). Ask for GMSZ College or Josef Attila Leany College.
The city is quite interesting and charming. It is a baroque town also famous for its wine, Egri Bikaver (Bull's blood). Even though it is small, it is worth staying at least 2-3 days, or a lot more if you use it as a base to visit the surroundings.