The prevailing winds blow the smog from the Sacramento Valley into the Foothills. As a result the Grass Valley Nevada City area has a problem with ozone. You might not see it, but the local air quality district knows about it and regulates the air in an attempt to mitigate it. For more info see the following.
Nevada County Ozone
As for stuff to do with the kids, that shouldn't be an issue. You should be able to find all of the activities you mentioned plus more in the area.
What you might want to check out is kvmr. Its the local community radio station. If you live out of the reach of there signal, you can listen to them online. There you can here about activities for kids. On kvmr, I have heard them mention classes for people in your situation who are interested in living on a big home in the country but don't know what is involved. They tell you what plants grow in the area, how much water you need from a well and everything else that is needed if you wanted to buy some property and build on it. So I know there are classes in the area available, but I can't find a link to them right now. But once you get up there, someone should be able to direct to them or if you listen to Kvmr, you can probably get a referral.
Welcome to KVMR 89.5 FM Music of the World. Voice of the Community. Nevada City, CA 95959
Grass Valley has a lot of charm, but I am not sure its for everyone. Grass Valley is an old mining town where the mine has been closed. As a result housing was really cheap there. During the 60's, in a back to the earth period a bunch of hippies moved to Grass Valley and Nevada City. Some came up with gainful employment. You can find people who blow glass, make soap, do a lot of arts and crafts stuff, they opened up a bunch of tourist shops and bars. They also started the grass valley group, a company that makes specific effects for television companies and a couple of companies in that area are spun off from the grass valley group. But they also grow a bunch of weed in the back country. If you listen to Kvmr, you will notice a lot of the sponsors are people who are selling stuff to semi-underground marijuana economy. A big reason people move up there was to get off the grid and compost is to cover up the fact they are operating marijuana fields.
In Grass Valley and Nevada City, you have this former hippie subculture living among the Christian home schooler crowd without a lot of middle ground. If you were looking for some hippie town like what you might find in Marin, or Mendocino, you might really like it. But you might also really be bothered by the marijuana growers and as result not feel particularly safe.
Depending on your attitudes you might think grass valley is a wonderful place or a horrible place to raise a family. You have community theater, it has its own natural foods coop, for all of those type of reasons, some people really like the area and think its an ideal place to raise a family.