Carl's point is a good one - go to a coffee shop or a cafe that doesn't serve alcohol.
Another option is to simply not go. If you have cancelled before it's not going to be a big deal if you cancel now - and you have a very legitimate reason to do so if you fear that you'll not be able to abstain.
A question you could ask yourself is what the real nature of the "night out" is. Is your friend expecting a night of drinking where you might also get something to eat, or is it truly a meeting to eat dinner? There is a big difference. And if it's the former, I'd definitely skip it - expecially just 3 days in. You've done some good work to get those 3 days under your belt, if it's too risky i'd just stay home.