If you have actual friends already, that’s a good place to start. After that, you can post on Craigslist (not recommended if you’re looking for a male partner, because you’ll have to wade through 10K penis pictures before finding a guy who wants to get coffee before whipping it out, and then there’s no guarantee it’ll go past coffee), or a site like OkCupid or possibly Match.com (I have no idea if Match.com has a FWB selection, and it does cost money). I don’t personally recommend PlentyOfFish, because it puts almost all of the entire initial focus on the picture, and the forms are much more freestyle, so most people don’t put that much and what is there isn’t real quality. And there’s always just finding guys the same way you would for a relationship, but making it clear to them that you aren’t looking for a relationship at this point in time.
It’s really important to figure out just exactly what you mean by “FWB” and “non-romantic”, and exactly what you do and don’t want this relationship to look like. It can be very hard to distinguish the difference between a close friendship with sex, and a romantic relationship – especially if your romantic relationships aren’t as traditional as a rom-com movie. For example, if you go out to movie and a dinner with this guy, is that a problem? Would it be if you were just friends, no sex? What if he gives you a birthday present? What if one of you confides in the other about the familial issues and drama you’re going through right now? What exactly about romantic relationships is it that you’re looking to avoid – with me, aside from some issues I have with traditional expressions of romantic love, I don’t want a “serious” relationship. I want a committed relationship, in which we care about each other seriously, same as how I’m committed to seriously caring about my friends. What I don’t want is this pressure to always be moving forward with a relationship, instead of finding that nice place where we get together a few times a week, spend a few nights together, but each have our own places, our own friends, own careers, own hobbies, own lives, and aren’t on a course towards moving in, getting engaged, married, buying a home, and then baby. I think it’s my own kind of long-term relationship, but to many, if not most, it’s casual dating or friends with benefits.
@Cruiser Friends with benefits, emphasis on the ‘friends’ and differentiation between just a hook-up or NSA sex buddy, is often just as emotionally intimate and focused on connection as traditional romantic relationships. The difference is mainly finding new (well, “new”, non-traditional is a bit more accurate) ways to express the intimacy and caring for one another, and finding a relationship model that works for the people involved, not Kate Hudson and Matthew McConaughey or the rest of society. To say that in all or most of them there’s no romantic attraction is only true if you’re going with a very narrow and traditional view of romantic love – which is the sort of exclusionary views that drives most people to seek FWB relationships in the first place.