Hey guys help me figure this :

On and off I get some messages from Japanese girls in Mixi to go out somewhere ....

Having lived in India gifts one with a heightened sense of paranoia.
After all you have no idea who the sender is, or if "she" is even a girl. Down there, it's not unheard of to lure a horny berk out and harvest him for body parts.

Some I savvy, insurance/pyramid schemes, wierd contraption (usually electro magnetic but so far noone's sold me a tinfoil hat)
& snake-oil sellers (cialis/viagra/"herbal" remedy equivalent for those connoisseurs of spam) abound.

Then there are the entrepreneurs ... trying to get you to join up in some business scheme that even acomu wouldn't touch with a dead stick.
Or the mixi link-whores ..trying to get connected to every last person in mixi.

Now some I don't get at all. They seem to be real. Their intros are believable, and they have friends who appear equally legit. They have a footprint in mixi. However they tune out when you say you're no longer in Japan :

What's their motivation? : Some guy to treat them to a free dinner in an expensive restaurant? I don't mind I guess but hmmm ....
Anybody actually accepted such invites?

It sounds like they are probably legitimate people, just looking for more Japanese people to expand their social network with - but just not interested in gaijin.

hmmm unlikely. I never hid the fact I was a gaijin in my profile. My profile even has my oh-so-very-non-Japanese mugshot front-and-center.