просто "идти по улице" (= along the street), хотя иногда может означать и в сторону уменьшения номеров домов
https://www.usingenglish.com/forum/threads/32632-Up-and-down-the-street

You took the words right out of my mouth.

+++Russ

Pretty woman, walking down the street. Pretty woman the kind I like to meet.... Who knows the original singer without googling? ))

I’ll give somebody else the chance to answer :-)