Well... hmm, tricky.
Firstly, avoid perambulate most of the time. It's almost archaic and not in general modern conversational usage. About the only time I can imagine it being used nowadays is to describe a tour of inspection, such as a General perambulating along a line of soldiers, checking how well presented they were, and even then it feels unnatural.
"Perambulate" perhaps implies no general direct destination. One would perambulate "around a park looking at flowers", or "through a wood", "along a path", but not "to the shops". One could "perambulate through the park on the way to the shops" though. It's about the experiences on the journey, not where you end up - and the origin of the word should give you that clue: from the Latin "perambulare" - to walk through.
It's a gentle walk, it is not hurried or forced. In modern English it's probably better to use a word or phrase such as stroll around, meander or wander.
A stroll can have that meaning, but can also have a destination - one can "stroll down to the shops". A stroll is still a gentle kind of walk, though.
I hope that helps.
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