I'm actually a bit hazy on the legality of it, as well. Personally, I think a private business should be able to cater to whoever the hell they want, but I'm not sure what the laws are concerning that. I know that there are places which will only admit men or women, and nobody seems to have a problem with that. Public facilities are of course a different story, as they should be.
As we all know, I can't stand kids, so I'm pretty cool with this. I will be interested to see how it plays out, though. One concern is that if they're successful, lots of other establishments might follow suit, and I wouldn't really like that. It'd be up to the market to create specifically family friendly places, and who knows how that'll work out.
Airlines are and should be a different matter. Yes, kids on planes often suck, but there isn't a viable alternative.