The border zone is within walking distance of the hostel.
The border zone is clearly marked with warning signs in the terrain. Entry into the border zone is prohibited and the area is monitored electronically. I can assure you that the monitoring works in this area, and various consequences have been handed out to those who have tested the rules.
From the edge of the border zone you can see the fells of the neighbouring country, so if you have never seen the Russian side before, here is an excellent opportunity — even if from a short distance.