I already know about coinbase.com
Are there other very large (and hopefully safe) exchanges that I can easily buy (and store in cold storage) bitcoins with funds from a US bank account? If possible I would like to just find out the largest 2-3.
There is Circle.com from reading this
http://www.coindesk.com/information/how-can-i-buy-bitcoins/"Circle offers users worldwide the chance to store, send, receive and exchange bitcoins.
Currently only US citizens are able to link bank accounts to deposit funds, but credit and debit cards are also an option. Apps for iOS and Android are now available." and that's your case.