1) Metro station "Tulskaya" (the last carriage from
the centre), leaving the metro station turn back and go to tram
lines, then turn to the right and go straight to the monastery.
2) Metro station "Paveletskaya", take any tram till
the stop "St. Daniel monastery"
St. Daniel Monastery on OpenStreetMap
The monastery opens for visitors from 6:00 to 21:00.