I think Superman drinks coffee, but it’s decaf. The caffeine wouldn’t do anything for his Kryptonian physiology.
Batman probably avoids caffeine because it can make you twitchy and unfocused. If he drinks anything, it’s probably tea, either courtesy of Alfred or some obscure medicinal brew he discovered on his travels.
Wonder Woman seems like a tea drinker too, though I’m not sure what specifically gives me that impression. Could’ve picked up a taste for soda while working at Taco Whiz, though.
Speedsters are too hyper on their own to need caffeine, but I’ll bet chronically-late Barry Allen got into the habit of drinking coffee or soda before he became a speedster. Wally would drink soda for the extra calories.
Hal, Guy, and John seem like coffee guys. Kyle seems like a soda-drinker. Don’t know as much about Simon or Jessica, but I’ll guess coffee and tea, respectively.
Damien definitely drinks tea, but I wouldn’t put it past him to partake in a soda to fit in with the Titans, or drink a coffee to try and be more adult.