I phoned Wells Fargo from Australia, I rang the number on their web site and they put me through to the branch at 791 N Nellis Blvd Las Vegas, I had already set up a Nevada LLC and had an EIN number, but they would not open a business account for me as I did not have an ITIN number, but they said I could open a personal bank account with them, and I did not have to go into the bank, did it via email & phone.  They post any mail direct to me in  Australia. They are quite a distance from the strip, the Wells Fargo at Howard Hughes Parkway Branch would be closer if you are staying on the strip.

I emailed Citibank at 495 E Silverado Ranch Blvd Las Vegas, they would open a business account for me  but I needed to visit their branch to open it, they were used to foreign people opening accounts there, as he told me  he had already had others there that week. I made an appointment with them,  I  needed Passport, Drivers License, a bill with address and phone number (an Aussie phone bill was ok)  and I took all the paperwork for my LLC .

They wanted an American mailing address for my statements to be sent to, ( I use the mail service that the people I got to open my LLC run).  This branch was quite a way from the strip too, you'd need to get a taxi.