Hiking around Eger and in Hungary

I don't know any either but I see groups walking around the hills here. 

You could try  Googling the Hash House Harriers (also known as 3H or HHH), which is a "drinking club with a running problem". It's non-comepetitive running. They also have a walking group so you don't have to do the run if you don't want to. The walks are usually 2 to 3 hours long and at weekends and are set up in advance/marked. There's a fee, but it's really low - just a few Euro - and is used to pay for the beer/drinks at the end. For anyone new in town, HHH is a very good way to get started on contacts.

Personally I've been on 3H walks in places as distant as Azerbaijan, Egypt and Kosovo. Always been very pleasant and you meet very interesting people.

If anyone knows of an MTB (Mountain Biking) group hereabouts, I'd be interested.