[GoNative]

No problems buying a place in Japan if you're a foreigner but it won't help you with getting any sort of visa. Up where I am over a 1000 foreigners have bought apartments and houses at and near the ski resort I work at. I've bought a house myself and had an investment property which I've since sold. You pay the same land taxes as any Japanese person would and they are pretty cheap generally.
In terms of getting a visa though as I said it doesn't make any difference. If you had a business running out of the property you could look at getting an investors visa but that doesn't really sound like what you're after.
I'd add that if you're looking in a scenic rural area prices are generally really, really cheap for houses but to be honest on the whole I don't find the quality of most Japanese houses I've been in to be all that great. Building a new home though is not all that cheap especially if you are looking for some of the things you'd expect in a more western style house (like decent sized kitchens and bathrooms and open plan living).