Fantastic. My children have loved one of Miyazaki's earliest films, My Neighbor Totoro, since they were 2.
This was no different. The story was simple, sweet and about as positive as you could get.
There were very few situations that were "tense" and put any of the characters in great danger, so if your kids are older and they thrive on having some major "bad guy" in a movie, this isn't for them.
Personally it's a favorite movie for myself, and for my 4 year olds. They loved it and wanted to see it again.
The pro-environment messages are good, I'm getting a bit tired of them, simply because they seem so forced, however they're a bit too subdued here and never really fleshed out to the point that little kids would GET what they were hinting at.
And the ending... Let's say it's far from the best ending Miyazaki has given in any of his movies. But at the end, it doesn't ruin the rest of the film, which is fantastic.
The worst part about all of this, really, is the lack of response. There's been so little interest here that it makes me fear for movies in this quality. The same thing happened with Spirited Away, which was a fantastic movie as well.
If you get the chance, and have kids that love sweet, endearing and funny movies, this is it.
It's "The Little Mermaid" with far more heart and less of a bratty main character.