Business banking outside home state?

I am starting an internet service business, which I have registered the LLC in Wyoming. Although I reside in Illinois, I travel all the time for work and would like to maintain my Wyoming corporate tax status (no corporate income tax). I was thinking that I should try to find a business bank account outside of Illinois at the very least, and preferably an account in Wyoming.

Does anyone know of a bank that will allow me to open and conduct business via fax and email? I'd prefer to find one in Wyoming.

Thanks.

I know Wells Fargo do remote banking, I have a business account in Nevada and one in Delaware (which is still Wachovia) but I live in California.

Have you looked into nationwide banks, like Bank of America? Surely they have at least one branch in Wyoming...and they'll have a ton of branches in Illinois. That way you'll be able to do business in both states, and any other place you may travel.