You can access your Canadian accounts in the US if you have an ABM card with the Cirrus or Plus logo. You can even use an ABM card in Mexico to withdraw from a Canadian account.
Canadian banks do offer US dollar accounts (the money is kept in US dollars and not converted to Canadian) but usually US dollar accounts do not allow withdrawls thru ABMs.
To get a US bank account thru TD you have to open a brokerage account with TD Waterhouse but they have recently made this a lot harder to get due to US banking regulations.
TD & Royal have US affiliated banks but they are totally separate entities and you still have to meet US banking regulations (Social Security card etc…) to get an account.
What you need to do is get a TIN number. To get this you will need the IRS form (available as a pdf), and you will need to get your signature verified at your us embassy or consulate. With that you can then open a US bank account. Some banks are better at knowing this then others. The best choice is often stock companies that offer a checking account as your money holding vehical, as they are often more aware of how to handle this then most banks are.