Over here you will hear "I want a cold drink" or give me a coke which also means soda in general here too.
Me when I first moved from NJ to NW FL many years ago (or South Alabama, as we sometimes called it):
In a casual restaurant:
Me: What's a po-boy?
Waiter: Excuse me?
Me: I said, what's a po-boy?
Waiter: You're jokin' with me, right? You really don't know what a po-boy is?
Me: No, I'm not joking, what is it?
Waiter: [explains po-boy]
Me: Oooooh! A sub!
Waiter: What?
Me: Nevermind - I'll have one of those - a po-boy, please.
Waiter: OK. You want a co-drink with that?
Me: A what?
Waiter: A co-drink. You know - A drink that's co.; like with ice.
Me: Ooooh! OK. I'll have a coke.
Waiter: OK, what kind.
Me: What do you mean?
Waiter: What kind o' coke did you want? We got orange, sebmup, ...
Me: Wait - what was that second one?
Waiter: sebmup
Me: Well, what's that like?
Waiter: Now, you really are funnin' me - sebmup - everybody knows submup! Comes in a green bottle, got a big seb'm on the front!
Me: Ooooh! Seven-up! No, no I just wanted a coke.
Waiter: Yeah, I know, what kind?
Me: Just a coke! You know, a coca-cola!
Waiter: OK. Comin' right up. *goes away muttering somethin' about damn yankees*