The restored stone ramparts of the Kuznetsk Fortress are massive and topped with cannons, but represent only 20% of their 1810 extent. Kids ride ponies around the attractive grounds, concerts are held and there are couple of modest museums that you can pop into – the archaeology museum, which contains mammoth tusks and old stone tools, is probably the most interesting.
The fortress is in the old part of town on the right (east) bank of the Tom River. To get here take frequent bus 5 from outside the bus station and get off at the first stop over the bridge (15 minutes). It's a 15-minute walk up the hill to the fortress via the beautiful 1792 Transfiguration Cathedral.