巡る and 辿る: touring places and following a path or trace
Compare touring temples with following an old path or footprints, distinguishing places visited from the route or clues followed.
Going around several places
巡る, read めぐる, can describe touring several places. 古い寺を巡りました。 says that someone toured old temples.
展示室を巡りながら作品を見ました。 says that someone viewed the works while going around the exhibition rooms. It gives both the area visited and the viewing activity.
Following a route or trace
辿る, read たどる, means following a path or trace. 昔の道を辿って村へ行きました。 says that someone followed an old path to the village.
足跡を辿って、小屋を見つけました。 says that someone followed footprints and found a hut. 足跡 gives the trace followed, and 小屋 the object found.
Places toured and clues followed
In 道を辿る, 道, read みち, is the path followed. In 寺を巡る, the temples are places toured. The noun has a different relation to each verb.
案内図の道を辿って一つの寺に着きました。 says that someone followed the path on the guide map and reached one temple. It does not establish a tour of several temples.
What guided the movement, and what was found, in 足跡を辿って小屋を見つけました。?
Show the answer and why
The footprints were the trace followed, and the hut was what was found. The sentence does not describe touring several huts.