Only go to places that maintain an illusion of hygiene and prices will rise fast. For example, you might pay the equivalent of $3 more per meal for a place whose employees wear gloves. But in reality, the dirty-looking place next door is actually cleaner; they throw lemon juice on their boards after cutting meat. At the same time the nicer-looking place lets raw chicken touch everything while handling money with the same gloves they use for food.
The hotels that cater to Westerners typically charge a lot more, and rates are more comparable to hotels in a cheap European city. Theoretically, with them you get a guarantee of food that is prepared with better safety standards. Whether this is practically true I have no idea.
Ironically, the cheapest way to live and eat in India would be to rent an apartment and get a trustworthy cook to come in and cook fresh food for you every day. Your daily bill will be way less than $20. However, setting this up requires a fair amount of legwork and contacts, which (understandably) someone who is looking for a vacation will not find attractive.
I met a seed-stage startup person who has this setup (somewhere in India) while traveling through a hostel in SF recently. Two meals cooked per day and cleaning. It sounded like a great setup and much more affordable than what that would cost in the US.
Anecdotally, working in Maharashtra with Indians in an Indian company for a few months I was never ill. This was eating $1 "luxury" 8 course meals brought to me in the morning by a dabbawalla on his motorbike which - as with all my co-workers' food - stayed out in the searing heat for a few hours before lunch; I also eventually had him bring me dinner. I lived in the same company housing as everybody else. No idea how you'd find a dabbawalla though, I just took the stack of leaflets dropped at the office and tried them all until I found a good one.
Coming back for 2 weeks to Mumbai, Delhi, Pune, Bangalore staying at a famous and very nice 5 star hotel chain and eating only in their restaurants, I caught the worst bout of my life. Bit wary of hotel kitchens since then.
- NYC? Get a bagel with cream cheese, or a chopped cheese ($3).
- Idaho Falls? Go to Reed's Dairy and the bakery by the public library with free samples (can't remember the name.) Amazing stuff, and pretty cheap.
- Netherlands? Cheese is pretty cheap and good quality everywhere in the country. Bread is incredibly cheap, and even if you're literally surviving off change you find on the sidewalk you can afford it.
- New Hampshire? Go to Cabot Cheese. Best cheddar in the world.
Of course also remember to eat fruits and veggies, but those are always cheap. I just bought 3 large peppers and a kilo of apples for €1.50 here in the Netherlands.
Definitely not the best, even in New England, let alone the world
Cabot cheese is the best cheddar though? That's fighting words if you grew up near Wisconsin. If you're ever near there go to Bobby Nelson Cheese Shop. The aged cheddar is amazing and they make their sausage.
Have you tried Cabot's whole assortment? For a few weeks a year they lay out a truly ridiculous assortment of cheeses, all free to try. Their hyper-local stuff kicks the ass of the (still fantastic) Cabot you'll buy in the grocery store. What you guys get in Wisconsin trucked across the country is probably not even close to what I ate when I lived a stone's throw from Cabot.
Also, my tastes run seriously sharp. Does Bobby Nelson have anything really sharp? If so I've got to check it out.
Secretly, my favorite cheddar - which I'd bet trumps Bobby Nelson, even if Cabot's hidden stuff doesn't - is made by an older woman who wraps all her cheeses in black paper and sells them at various markets around the Quechee Gorge. But it's somewhat expensive and very hard to find. The last time I bought some I weighed it before and after eating to make sure nobody else touched it, it's that good.
If you want to get more global, try obscure Welsh cheddars. Amazing but expensive. They go very well in between scotches.