When I was last there in May 2015 the Joffreys stations were still around and they make very good iced coffees IMO. I'm not sure if they're any cheaper than Starbucks, but there wasn't a 50+ person line at the carts like there was in Starbucks.
Good point (though since coffee is both a tasty drink AND a caffeine delivery system I'll still drink it if I have no other choices (castor oil has no caffeine!)), but the OP is looking for iced.
She might consider checking out a starbucks for their iced coffee to see if she likes it. Gives her more choices.
Then again, if there's one thing I like less than Starbucks brewed coffee (please note I like their espresso drinks just fine!), it's whatever Dunkin puts in their coffee pots, so the OP's and my tastes do NOT align, LOL.
Outside of Starbucks most, if not all, locations server Joffrey's. I prefer french press to drip and the best I had last trip was at Boma. I do really like the Kona french press as well. I am not sure which blend they serve but the drip I got at the coffee stand in the contemporary lobby was excellent. I assume it was one of the Joffrey's blends but I wish I asked which one.
The Wave at Contemp also serves French press. If you're there for the breakfast buffet, you can request French press as one of your 2 beverages that's included with the buffet.