1.
to go a bit further; to make a side trip
To extend one's journey to visit a nearby place while one is already out. Literally "to stretch one's legs," but the Japanese meaning focuses on traveling a little further to reach an additional destination.
Usage
足を延ばす is used when you are already out somewhere and decide to travel a little further to visit an additional place. It implies the extra destination is relatively nearby and worth the small extra effort. Often used with せっかくだから (since we're already here) or ついでに (while we're at it).
Common patterns
Watch out
Do not confuse with the English idiom "to stretch one's legs" (meaning to go for a short walk to relieve stiffness). The Japanese expression focuses on extending a journey to an additional destination.