There are a couple of different things to do, but one of the challenges you're going to run into is that most non-profits are kind of too short handed (or short of time) to be able to go, "yes, of course, that'd be awesome!" (That's how many volunteers get turned away as well, actually). A lot of time when volunteers (or donations) turn up, the random employee being offered them is going to be searching their brain for a way to put them to good use, and if one doesn't immediately come to mind, there more likely to turn it down, because they've got more than enough on their plate with everything else. I've been in this position myself. I was working for a collaboration of 60ish non-profits, and someone wanted to donate an old copy machine to a non-profit. They didn't care which, just any one that needed a copier. And it was a pretty good copier, but still. The actually collaboration office couldn't use it, didn't have the room for it, certainly didn't have the money to get rid of it or move it if that became necessary. I sent out many, many calls to every agency I could think of, seeing if they needed a printer. And I'm sure, somewhere, one of them did. But if they had the need, they hadn't yet realized it, or weren't talking about it. And few of the newer ones, that were more desperate for resources, were willing to take the risk of it needing repair work or finding a way to move it from the donor's place to their office.
So here's what I'd suggest. If you have a few good non-profits in mind, ones that you know something about their operations, and there's something *specific* they could use those computers to address....I would offer it to them like that. "Hey, I know you were looking for a way to get the kids in the shelter a way to get on the internet for their homework, I've got some computers for you..." Especially if you can volunteer to provide support. That will actually probably be pretty welcomed.
Second, if you don't have any specific charities in mind, you could see if there's a local non-profit dedicated to fixing up old computers and giving them away. There's usually one in every county, and they'll have the relationships and connections to know who could use it and how to get it to them. I'm sure they wouldn't complain about having the work already done for them.
Third, you could try just contacting various groups and seeing if any are looking for computers. Good groups to start with would be shelters, churches that run shelters/food kitchens/that sort of thing, *domestic* shelters (especially if they have a safe house, but don't be offended if they turn down an offer to help set them up. They guard the locations fiercely, because they must). You could also try the local Girl Scouts and Boy Scouts groups (though I'd recommend avoiding the nearest council, and just seeing about getting in touch with the local volunteers in charge). After school programs might be good, as well as any programs dedicated to helping the elderly and disabled be more self-sufficient. Start by explaining that you've refurbished them (so they're not just "old" computers that need repair) and also, if you're willing to help set them up etc. And there you go.
You probably won't read this, as it'll be at the very bottom, but if you do, I hope it helps.