I'm not sure what the answer is for you really. (I doubt an alcohol-free bar would take off!)
What would your ideal be?
As others have said, it sounds like you'd like a night out dancing but for others not to drink. In which case YABU! Our nighttime culture does revolve around alcohol but not necessarily to excess. Particularly if you have to deal with children the next day! Unless they're all without children I find it hard to believe that they all get smashed every time. More likely just a few. You can't expect everyone to not drink at all.
You mentioned the theatre. Do you chat to people at work? When you're chatting why not suss out if anyone fancies going to a particular play? Maybe in a local theatre rather than West end. Cheaper and usually a short run so you'd need to set a date rather than 'one day'.
Going for coffee is trickier. It's a quick thing as people don't tend to have several. And it tends to be daytime thing. After work there are things to do like make dinner etc. And at the weekend I assume you'd want to spend time with your DC.
I've never been teetotal but don't always drink when we go out. I like to know how I'm getting home so I often drive. I don't need to drink to be happy and chatty so nobody would be any the wiser. And seeing everyone else drinking doesn't bother me either. I get my J2O when they get a drink and join in the dancing and general fun.
Someone mentioned sadly clutching an orange juice feeling excluded. Why? Everyone still talks, they don't drink in silence, you can talk too. Everyone goes for a dance, you can dance. Kebab after? You can still eat. All these things can be done with or without a drink.
Show everyone that you're just as much fun sober as they are drunk and you'll be included. Stand giving off vibes of disapproval and you'll be excluded. Sorry.