Buy the JR Rail PASS
Honestly, you want to go a lot of places in weeks, ~$450 USD (¥46,390) is what a JR Rail pass costs for 14 days. It will cost you at least $40 (¥4000 on sale) round-trip just to get to Tokyo and back from Narita Airport, so that drops your cost down to $400.
You want to go to Tokyo, Nagano, Toyama, Takayama, Nagoya, Osaka, Hakone back to Tokyo in TWO weeks? You're going to be on the move for 2 weeks, not staying in one place for more than a couple of days and that makes you a perfect candidate for a 14-day pass.
It's also good for any JR local rail transit, which will help in Tokyo as well if you want to visit Yokohama etc.
Remember, you're travelling at LEAST 6 segments. I doubt you'll have time to hitchhike to all those places and if you do, you'll have to be more flexible with your accommodations which may end up costing you more. Sure, cheap buses are available, but given the number of destinations you have planned, the train is a much saner option.
In short, taking the train may SEEM expensive, but I am willing to bet that trying to visit that many places in that short period of time... The JR Rail pass will end up being the best for your needs.
Are Japanese trains REALLY that expensive?
Japanese trains seem expensive because they don't run them like an airline or like European train systems, which charge an arm and a leg for last-minute travel, have complicated ticket classes each with their own rules and offer deep discounts to attract people to book far in advance.
For the most part, Japanese trains are run like a commuter rail system. The price doesn't fluctuate that much, is set at a consistent price, and is extremely flexible, which is why the JR rail pass is perfect for your needs. If you like a place and want to skip the next place, you can feel free to do so without worrying about getting your money back for a bus trip.
Besides, how can you go to Japan and NOT experience what is arguably one of the key defining aspects of modern Japanese culture, the bullet train?