I'm all for adoption centers; it's going to be a lot harder to organically find a cub/pup/foal/grub through RP than a mate (though it happened to me, so... I'unno). And food stands are just fun; no reason not to like those. Mate centers seem... like they're missing the point of RPing and having a mate at all. But if you REALLY NEED to RP with a mate right this minute for some reason, I guess do whatever floats your boat. This is coming from someone who's not into the whole mate thing in any context, so I may not be the right person to judge that.
Divorce centers, though? I didn't even know that was a thing, and now the world seems a slightly more dismal place. WHY, in the name of sanity, would anyone ever need one of those? Your FeralHeart character isn't actually you and there's no legally binding contract; if you don't want your character to have a mate anymore, tell your RP partner that you don't want to continue the RP! If you actually feel the need to have your character get a divorce to break it off, you are getting WAY too invested. Unless said divorce is a plot point in a long-term RP or something, but in that case a divorce center probably still isn't necessary.