I don't live in India but visit every year. My mom gets super protective about me at that time. As a grown up, I have no restrictions on how I dress up and where I go out, but when I go to India, it's all "mom knows best".
When I visit my relatives in UP, I have to wear loose fitting shalwar kameez and not go out alone. There is a bunch of female cousins or a male cousin with me at any given time. I'm often told to not make eye contact with men so that I don't become aware that I'm being gawked at and hence don't feel uncomfortable. But I always make eye contact because to my mind, it is dangerous not to make eye contact when you're outdoors. Often, I feel helpless during my vacations because I'm stripped of my basic freedoms. It's a self-respect-losing kind of helplessness. Like, if I have to just get soda from the market, I can't just go by myself because respectable girls do not do that. I'm under the mercy of whoever is available at home to oblige me. Once, my nine year old male cousin tagged along because none of the older men of the house were available to go with me to the market just down the frigging road. I saw my nine year old cousin's chest inflate with pride that he was given the responsibility of escorting his 20 year old female cousin. That belittled my self respect a lot. As if he'd be able to do something if anything bad were to happen. Most likely I'd be saving his tiny ass.
But the feeling of pride he felt is the crux of the problem. Patriarchy demands boys to become men. To become saviours of good, virtuous women who have the decency to not go around unescorted. Conversely, it is loose women with zero morals who walk around freely, wearing whatever they like who are not worthy of respect and hence fair game.
Sadly, most women themselves choose the convenient route of conformity. They are quick to label and ostracise another woman who doesn't fit the code. Patriarchy perpetuates.
Sorry, I did not mean to write an essay but I got worked up. My answer to TM's question is that I don't feel safe in UP/Delhi (Bombay is fine in parts) but I never too overwhelmed because I know I'm only there for holiday.