Yes, drink mixers at most bars will all have aspartame. Generally, if you drink aspartame in moderation it shouldn't be a huge problem. Other good choices are wines, LC beers (some light beers are okay... I think Miller Lite is only 3.5 carbs), and cocktails without sweetened spirits aka Martinis.

I usually just go with rum & diet coke and don't worry too much about the aspartame.

Have fun in Hawaii!