Out of those I would personally pick Stans. 20 minutes to Luzern centre on the train, not far from a whole bunch of ski slopes/Wanderweg in pretty much any direction you choose to drive. We have friends in Kriens and I don't like it much - but then I'm not a big fan of cities. Stans is more like a small town, surrounded by greenery - at some times of year there are cows grazing pretty much in the town centre, which always makes me smile.
Hergiswil is lovely and of course much closer to Luzern but I have a feeling it might be rather dark in winter due to Mt. Pilatus. Could be seen as a good thing too - less heat in summer!
We live up the hill from Stans, which means we're not in the Stans school but the local village one, which we love. (It's also worth considering the villages, as they only add an extra five minutes to your commute. If you're not relying entirely on public transport, that is. Lots of expats in Buochs to the east, with plenty of shopping facilites etc; excellent and foreigner-friendly primary school in Ennetmoos to the west but then shopping has to be done in Stans.)
But to be honest apart from Kriens I'd be happy for our family (2 small children) to move to any of those; you might be better off basing your decision on what accommodation you can get for a reasonable price. Although housing is supposed to be cheaper north of Luzern so perhaps that's not something you're concerned about.