Take a look at each of your options and then consider safety and ease of use.
For example, what is your bank charging to use an ATM? Many report having to pay $5 for using an out of network ATM plus a 3% Foreign Transaction Fee. Currency exchange will be at interbank rates plus about 1% typically. What this means is that if you take tout the equivalent of $200 of TL, you will pay about $12 or 6% ($100 would cost ~9%, $300 about 5%)
How does that compare?
An ATM card with no bank fees and no Foreign transaction fees would only cost about 1%
A credit card with no foreign transaction fees would only be about 1%
A Credit card with Foreign Transaction fee is typically 3%
Getting some TL here in the states would cost at best 5%, up to about 8% if you go to a bank. You would however have to estimate what you might need, risking over or under planning, and you have to carry all cash with you.
Taking US Dollars and exchanging there is not a bargain. You might be able to get as good as 4%, 6-10% would not be unusual, again, you have to have the cash with you.
In the end, it would certainly be best that you have a better ATM card. If you have a Credit Card with no Foreign Transaction fee, or even if it does have, use that for larger transactions and really any time you can.
For cash however, using your ATM card even with the fees is the best option.