Building US credit rating for foreigners
 

I have a US SSN from a short stint I did working in the USA several years ago, so I would like to leverage that to obtain US credit cards. I'm happy to start with a secured credit card (I know some providers will issue one for as little as US$500 security) - small limit is fine, since the main motive is to develop a credit score.

Is US state ID a must though? If so, how can I get one?

No ID required, the SSN and a real physical mailing address in the US is sufficient. A checking account in the US is helpful, but you need to be personally ID-ed (foreign passport is OK) for that. You might want to download the existing credit rating report to see how the bank rate you currently. Anything credit like that happened >6 years ago make you credit card worthy.
Avianca Lifemiles offers secured credit cards that earn miles, BTW.

More here:
http://www.flyertalk.com/forum/ameri...dit-cards.html
http://www.flyertalk.com/forum/credi...in-no-ssn.html
http://www.flyertalk.com/forum/credi...residents.html

So If I visit the US, can I just walk into a bank as a foreigner and say I want to open a checking account and be accepted? Or do they tend to be strict?

You don't live in the US and you are not a US citizen? You can not legitimately acquire a US ID. You'd probably end up flagging Homeland security.

I did my MA in NYC. I bank with TD in Canada and went to a TD branch in NYC.

They wouldn't open an account for me unless I gave them a piece of mail with my address on it and name. Or I had to get the university residence to write a letter and bring that in. I didn't bother as at the time the exchange rate was 1:1, and TD didn't charge any fees for using the ATM in their US branches.

Without a mailing address I am not sure you can open a US bank account. They wouldn't let me.

As mentioned above, you need a US mailing address and proof thereof (ie some other document addressed to you at that mailing address).