Not that long ago, one could exchange traveller’s cheques at hotels and travel agents. The only problem I experienced was in Assam, where I ran out of money. I had to wait five days until the one and only bank (in a city of 1 million!) opened again. I even managed to cash a cheque 15,000 feet up in the Himalayas! But alas, American Express traveller’s cheques are no longer issued nor accepted.
Credit cards are accepted at most tourist centers, particularly the more expensive hotels and gift shops. Although more banks are offering ATMs, the few examples that I used were woefully unable to process my foreign card. Most of them don’t even work. Sometimes you will have to try several ATMs before one will obligingly spit out cash.
Another option is find out which bank cards are accepted in the area of India you are travelling to. If you have an account with one of those banks, you will have access to your cash. If not, then open an account in one of the accepted banks and put in enough money for your trip plus extra for emergencies.