3 week itinerary in December feedback

Hi, we're a couple early thirties, interested in seeing the sights, scenery, pop culture, etc. We've shortlisted budget accommodation options, private rooms with shared bathrooms. Here is our planned itinerary:
Tokyo 4 nights from 29/11,
Explore city,
Day trip to Mt Fiji,
Day trip to nikko,
Tokyo to Osaka by plane,
Osaka to Kyoto by train,
Kyoto 4 nights from 4/12,
Explore Kyoto,
Day trip to nara city by train,
Day trip to himeji castle by train,
Overnight in koyasan maybe,
Kyoto to Takayama by train,
Takayama 2 nights from 8/12,
Explore town/region,
Takayama to yudanaka (Nagano),
Yamanouchi Town 7 nights from 10 /12,
Explore town,
Skiing Shiga Kogen,
Jigokudani Monkey Park,
yudanaka to Tokyo by train,
Tokyo 1 night on 17/12,
Q's: I have priced all the train journey's on Hyperdia and doesn't look like JR pass will save us much money, have heard pass doesn't cover all journey's anyway, can you buy train tickets on the week or day of travel? Are the train prices higher if purchased on the week or day of travel?
I am undecided on overnight koyasan, depends on available time and costs adding up, if we go might do it from osaka then onto kyoto.
We're thinking of dropping takayama due to preventing further budget blowout, have already increased budget.
Is Yamanouchi town an okay base for skiing Shiga kogen, we've both never skied before, will need lessons and gear hire, looks like there's daily buses from yamanouchi to shiga kogen, hard to tell frequency.
Any other hints, tips, recommendations welcome, nothing is booked yet.
Thanks!

Are you sure you are using cheap accommodations? Or are you planning a feast somewhere? Japan is not that expensive. Check on the webpage on budget traveling. Like Traveling by coaches or even sleeping on night coaches.

Japan Rail Pass is for intensive travel over 7 days. You are not travelling far enough over the 7 days for it to matter.

You are not spending enough time in Kyoto. You are effectively spending a day sightseeing Kyoto. KoyaSan is an amazing place. Takayama and Kanazawa are fascinating places. But if your budget can't up hold up, there is nothing that can be done. If you get a Kansai Pass it might help to lower your costs.

My only recommendation is to get more cash before planning japan. Or cut short your holiday so you get to experience each city properly and not rush to get to another city.

Do you need assistance in finding accommodation or places to eat? If you could show us your cost breakdown, that would help.

Why do you use plane from Tokyo to Osaka?
Assuming if you do drop the Takayama section, one way you could do it is:
1. Purchase JR 7 Day pass and activate just before you leave Kyoto
2. Travel back to Tokyo before the end of the 7 day pass.
3. Purchase JR Kanto Area pass
3-2. Use JR Kanto Area pass to visit Nikko (Optional due to issues, see below)
4. Use JR Kanto Area pass to get as far as Karuizawa and buy separate ticket to Nagano. (Nagano - Karuizawa, 3480 Yen)

Kanto Area Pass: 8300 Yen

Tokyo-Nikko: 5380 Yen
Tokyo-Karuizawa: 5710 Yen
Karuizawa-Nagano: 3480 Yen
Tokyo-Nagano : 8000 Yen

Biggest issue is you are staying at Yamanouchi for 7 days. One way to do it is to purchase 1 Kanto area pass and combine your trip for Nikko then to Karuizawa and purchase a separate ticket to Nagano from there.

So known ticket as follows:
JR 7 days: 29110 Yen
JR Kanto Area Pass (hopefully include Nikko): 8300 Yen
Separate ticket to Nagano: 3480 Yen
Trip back from Nagano (ticket) : 8000 Yen
(JR Kanto Area pass while require you to purchase extra ticket to reach Nagano, it allows you to make full use of the places you can go in that 3 days, which include Nikko, Karuizawa etc)

Not sure if it actually saves money, but definitely better than JR 14 days pass due to your 7 days stay in Yamanouchi.

Thank you for your suggestions, I had a budget in mind when I started planning a holiday in Japan, as you do with anything, I can increase the budget further though.
I was looking at flying from Tokyo to Osaka as it's a good price, unless I get a rail pass, the 7 day pass is not looking like a bad option now, can activate for side trip to Niko, then use to Kyoto and side trips there, I think I'll add some more time in Kyoto now too.
Do some train trips cost more if purchased on the day or week of travel?

Trains fee are fixed. Different trains have different prices though.

Though I say the prices are fixed, it does change. Every couple of months there will be a price update. The chance of getting affected by it is low though.