It may seem a contradiction, but if there's such a thing as haute cuisine junk food, Nathu's is it. This is street food for discriminating foodies. Great flavor and texture at very reasonable prices, with a hole-in-the-wall atmosphere.
If you prefer to avoid fried food, Nathu's doesn't have much to offer you. But if you don't mind a bit of oil in your quest for the best incarnation of North Indian street food, Nathu's can't be beat.
For example, don't miss the samosas with channa (which vegans should request without yoghurt), which are fried but don't feel too oily and have delightful taste and texture that make them a class above your ordinary samosa. And if your belly can handle an assault of oil, the chole bhature (chickpeas and frybread) here is peerless (though better shared with a friend, since eating the whole thing oneself would be quite heavy).
The most salubrious thing they serve is perhaps the seasonal (winter) special, sarson ka saag with makki ki roti (mustard greens with corn flatbread), which is beyond delicious.
There are oodles of sweets in the display case, but vegans beware: almost all of them have dairy of one sort or another (milk, evaporated milk, butter, ghee, yoghurt, etc.). One vegan exception is the sohan papri (but ask, just in case). If your server doesn't seem to have a confident command of your dietary restrictions, i'd suggest you go to the counter and speak with one of the higher-ranking folks.
Cons: Most items are oily, though some less so