USD account

Why are you surprised by this didn't you read the terms before you used it? There is always change for changing currency in any bank the easiest way is to find an intermediary agency who will move your currency and change it for you before depositing it locally they will also charge but it tends to be less. As far as I'm aware there is no way that you won't pay for this service but shop around for a good rate and low commission.
I know this is uk but explains choices
http://www.telegraph.co.uk/finance/personalfinance/11986097/Transferring...

I realise you're after usd here too so many be not what you're asking but you will struggle to find anyone working with a currency that isn't theirs and not charging is my guess and I'm unclear why you need a local usd,account you can't spend them here

Try opening a PayPal account in USA and another in Europe and transferring money between the two and then making a transfer from Paypal to your local account.

There are two elements involved. Commission and exchange rate.
The commission charge is normally fixed; the exchange rate can vary from minute to minute. If you find a bank offering low or zero commission they will apply a less favourable exchange rate.
You are going to pay for the service one way or the other. By the time you have checked out the rates offered at a range of banks and decided which is best, any or all of them can have changed.

Try https://transferwise.com/ - this is a transfer service that charges a small fee but takes the exchange rate of the day - so you gain a little. Have tried a number of times and works very well.

I have used transferwise many times and for substantial amounts and they are excellent, MUCH better than the banks.