Opening a bank account as a non-US resident in the USA

I am interested in parking some of my savings in a US bank account. My upcoming visit at the end of August is a good opportunity to do that because, a non-resident cannot open an account online. I know there are some options but, I would like to go with names, I am familiar with.

I am looking at Wells Fargo, Citibank and HSBC. HSBC is present in Turkey whereas the other two are not.

I am going to base my decision solely upon the following fees:

1. Account Fees
2. Fees for withdrawal from an ATM outside the US

Normally, if you maintain a certain balance, they should not hit you with fees. I have no intention to use this account in the next few years. No fees for a minimum balance of USD 1500 and 2-5 USD per each ATM transaction outside of US is acceptable to me which seem to be the norm from what I have read.

I haven't decided as to how much I would like to bring to the US. That is an important decision and I do not want to go overboard with that at least in the beginning. I am thinking of gradually shifting money to such an account.

If HSBC makes it easy and cheap to transfer funds between the two countries, I think, I will do business with them. Right now, I am not a customer of theirs in Turkey. I looked it up though and by moving some of my savings to an account with them might prove useful. I have submitted a form inquiring about what I need to know. I will wait patiently till someone gets back to me in 24 hours. Hoping at least...

Some of you may ask why I want to do this so, here is why: I am very suspicious about the future of the economy and political stability in my own country. I think the current government is screwing up big time and at one point they may decide to freeze our accounts, limit withdrawals (happened in Greece; a European Union Country a couple of years ago) or decide that our savings in foreign currencies will be converted to the local currency. Or even worse, a civil war may break out because of the stupidity of the Government.

Many people do not think any of this might happen but, I am a born pessimist. I would like to park at least some of my money outside of Turkey at a trustworthy organization yet still within reach globally. Better be safe than sorry...