There are just as many people who go out and do things unrelated to drinking as there are people who do.
You just have to know where to go to find them. And if you look pretty much absolutely anywhere that isn't a bar you'll find them.
Different kinds of people enjoy different kinds of places. That's all you really need to know to understand my point.
Drunks like bars. Weight-lifters like gyms. Readers like the Library. 'Avant Gardes' usually enjoy coffee houses or art galleries. Gamers and Computer enthusiasts usually like the movies, game stores, or stay at home and go online to talk to people.
You decide what you like, what kind of people you want to be around, and you go and do those things with those people. It's called 'finding people with common interests'.
I understand where you are coming from, as I can't even seem to get drunk even if I want to, and it does appear to be more difficult to socialize 'easily' when you're not doing what a lot of people seem to enjoy doing. However, if you simply realize that all these people are doing is sharing a common interest, albeit one which inhibits their impulse controls, then you will realize that socializing in general is usually very easy for everyone and that it only requires exploring ones' own interests.
While the effects of alcohol possibly do eliminate some of the fears of socializing and make it easier for people to open up to each other, it is not really necessary. One simply needs to commit themselves to forming lasting relationships and eliminate their own fears of opening up to others. It is likely that the people who enjoy drinking with others likely were somewhat outgoing or extroverted in the first place.
P.S. If you're unable to physically enjoy some things, like weight-lifting, then find something else that interests you. Know your own limitations. Human beings are not one-dimensional creatures. Explore and discover.