If you have arrived at an odd hour there are many hotels in Kolkata. You can pre-book a hotel room by phone before you come to India. The phone numbers of decent hotels are in the India travel guides some of which can be found on the Travel Planning page.
There is an economical airport hotel if you don't want to venture into the city. The Airport Plaza Hotel (Tarun Sengupta Sariani, Number One Airport Gate) has basic rooms that start at Rs 250 for a double room. There are rickshaws that will take you there for about Rs. 10. Ask for "Airport Plaza Hotel, pas may Ek Nambar Gate".
The Sudder Street and Chowringhee Road area is the tourist hotel area of Kolkata.
The Salvation Army Guest House (2 Sudder Street, Phone 245-0599), have doubles with private bath from Rs 200 to Rs 700.
The Hotel Maria (5/1 Sudder Street, Phone 245-0860) have single and double rooms with private bath for Rs 200/250.
The Capital Guest House (11B Chowringhee Lane, Phone 245-0598) has doubles with private bath for Rs 300 to 350.
If you get really stuck and can't find a room, try the YMCA (25 Chowringhee Rd, Phone 249-2192) It's a massive old place, and there are many stairs to climb, which is not a lot of fun if you have much luggage. It is also not a great value at Rs. 500 for a double, but if the other places are filled up, this place will probably have a room. It's the only place on this list that I have personally stayed. Meals are supposed to be included, but it's not veg. Tell them you won't be eating there and they'll knock something off the bill.