The surroundings of the Carthusian monastery in Červený Kláštor provide several possibilities for cycling. The most beautiful and closest is the bike tour from the museum through the Dunajec gorge in its canyon along the green to Lesnice, where the Dunajec rafting ends and the path continues along the red to the village of Lesnica. There, right in front of the Coop Jednota store, it turns orange (blue) and crosses the ridge back to the monastery. You can find everything you need at this link: http://www.mountainbiking.sk/sk/zoznam-cyklotras
You can also find all other options on these pages:
http://www.vitajtecyklisti.sk/cyklotrasy/16-tatry-a-zamagurie.html
http://www.opencyclemap.org/?zoom=8&lat=48.54202&lon=19.47412&layers=B0000
https://www.cykloportal.sk/cyklotrasy