Citizens of many countries, including the U.S., need visas to enter Turkey. You can apply for an electronic visa before leaving here: https://www.evisa.gov.tr/en/
Taxis are relatively affordable; although, not all speak English so have an address ready for them to view. There are several rental car companies right at the airport, you can book ahead of time on your traditional booking websites like Expedia or Booking.com.
Most stores and restaurants will accept major credit cards, though American Express is not widely accepted. It is advisable to bring cash as well.
We will be getting to Bodrum, Turkey the last weekend of May, and staying until a few days after the Wedding. We will be more than happy to extend the celebrations with you all heading up to the wedding.
There are lots of cheap direct flights to Milas Bodrum Airport from Istanbul. From Milas Bodrum airport take a cab or Havaş bus to Bodrum. A Havaş bus should cost 17.5 Lira, and a cab should cost around 150 Lira depending on your destination. All hotels will help arrange pick up if you call in advance.