Great Indian near Times Sq?
You might try El Nido's Bombay Eats. I've only had their food a couple of times, and not for a while, but I was quite surprised at how good it was. It's on 52nd St. between 8th and 9th Avenues. It's not exactly a hot location, and the place itself is fairly plain, though not storefront stark. Phone number is 212-265-7777.
For dirt cheap, great Indian lunch, Minar:
One of the best things ever to happen to my taste buds as well as my wallet was my discovery of Minar, in 1987, I believe. Minar is a cafeteria-style place that serves both north and south Indian food. I believe the owners are from Delhi. The south Indian items like dosas and utthapams are decent, but the northern items shine. The best deals at Minar are the combination plates. For $7.25 one can choose two meat and one vegetable item, $6.25 for all veg., with a choice of rice or bread (I highly recommend the naan). In addition to dishes made to order, there are at least 12 items available in the steam tables each day for combinations. The place is so popular that they’re always fresh. Some of the selections, among them lamb curry and chicken tikka masala, as well as some of the best aloo gobi (potatoes & cauliflower) and saag paneer (spinach & Indian cheese) I’ve ever tasted, are available all the time. In addition there are daily specials, one of the most notable being Tuesday’s sarson ka saag (spicy, pureed bitter greens), a Punjabi specialty traditionally served with a griddle-cooked cornbread called makki di roti, which I’d describe as something between a thick tortilla and a dense polenta. The only items to avoid are the kebabs and tandoori chicken, as they’re precooked and reheated. Minar is basically a lunch place, though they are open until 7:30 PM. There are two locations, one on 31st St. just west of Fifth Avenue, and one on 46th St. between 6th & 7th.
I eat Indian a lot while in NY but right in the Times Square area there's just a chaat house I go to for lunch, Sukhadia, 17 West 45th St btw 6th Ave (Avenue of the Americas) and 5th Ave, N side of the street, 212-395-7300. It's inexpensive and they have a real bargain buffet, but check with the lady behind the counter to make sure that the buffet that day includes chaat--otherwise order a la carte. Have the chaat with chick peas in what looks like a broken samosa or the batata vada, mashed potato balls. Also try the little dessert cakes.
If you want a good Indian dinner, consider Tamarind, 41-43 East 22nd St between Park Avenue South & Broadway, 212-674-7400, www.tamarinde22.com. But that is not in the Theater District. It's in the Flatiron area, not too far from Curry Hill (though it's much more upscale than the Curry Hill strip).
Or there's Bukhara, 219 East 49th St between 2nd and 3rd Avenue, 212-888-2839. Or Dawat, 210 East 58th St between 2nd & 3rd Ave, 212-355-7555, the place set up by cookbook author Madhur Jaffrey. But these are over on the east side of Midtown, not the Theater District.
Marginally closer to the Theater District, a bit overpriced but trendy and interesting (though not my favorite, it has an interesting menu that I've only begun to sample) is Bombay Talkie, 189 9th Ave at West 21st St, 212-242-1900, www.bombaytalkie.com. Open lunch & dinner; closed Mondays. This is in Chelsea, about 20 blocks south of the Theater District.
All of these places are walkable if the weather is good--at least, I walk it all the time, and NY is a walking city. But if you are not a walker, you can take a bus part way, or a cab.
As for the East Village, that is further yet. I've not been to Havelli, mentioned above, but there is also Banjara, East 6th St & 1st Av.