Opening a bank account in the US as a non-resident is very hit or miss. You can find reports of people who have tried and failed, and people who have done it successfully for themselves and/or for their US LLCs.
From what I've gathered, if you are visiting in︀ New York or Miami, your chances of getting approved are higher than if you are︁ elsewhere in the country (except maybe Delaware, and you want to open an account for︂ a Delaware LLC). Wells Fargo, JP Morgan Chase, Bank of America, and US Bank are︃ reportedly open to non-residents. In California, there are some smaller, regional banks that will consider︄ people from Asian countries but I'm not aware of any for Indians, it's mostly for︅ Chinese and Koreans and South East Asia.
Show up with passport, proof of address, recent︆ bank statement, and credit card statements (and the corresponding credit card). If you get rejected︇ just go to another bank.