I'm from Southern California and I just tend to call the drink by it's name. "I could really go for a Dr. Pepper right now" etc. Though, if I have to be general, I'll call it "soda".
My family is largely from Chicago. They tend to call it "pop" most of the time. One of my cousins lived in Mephis for a while and he noticed that they refer to everything as "coke" (as in asking the waitress, "What kind of coke do you have?" and she replies, "Pepsi, Dr. Pepper, Sprite and Minute Maid Orange")
.....Kelly