Indeed visa costs depend upon nationality and, like Brazil and the USVisit program, Turkey reciprocates what we do. If we charge a Turkish citizen $100 for a tourist visa to the US, they charge American citizens $100 for a six-month tourist visa to Turkey. That's the current rate for US passport holders.
I think they do require cash but you can get the visa at the airport, and they may be set up for credit cards now. I don't recall any luggage lockers, but that doesn't mean there aren't any just that I didn't need to use that service.
Taxis are not particularly cheap and the airport is a fair distance from the tourist sites. Depending upon the hours, I recommend you focus on a visit to Topkapi -- the least intrusive (in terms of ads) info site:
http://www.ee.bilkent.edu.tr/~history/topkapi.html
If you have any time left, you probably should take in the Grand "covered" Bazaar which is nearby Topkapi. Enjoy your visit!
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Cheers,
Greg