In hindi, aimless strolling is called matargashti. There's actually an amazing song by the same name from a fantastic movie called Tamasha, which is all about matargashti in life.
Great to see broadening of the discussion's cultural scope from red light districts and western tourism in Paris to parallel concepts. However, the definition I found online suggested Hindi/Urdu maṭaragashtī can also refer to aimless loitering... a much less romantic and far more prevalent activity in the subcontinent!
One of my favourite Indian flaneur moments was finding a safe-looking mushroom while circumambulating a hill near a Jain site I was visiting in Karnataka. Bored and of generally flaneurial mindset I decided to eat it. About ten minutes later I wandered past a push-cart in to a small village, and came across a fluorescent hot pink goat. I wondered if the mushroom had anything to do with it, and had to double take - but no: they'd missed a spot. The animal had been spraypainted! Only in India...