How to calculate and plan train rides?

Hey there Japan Travelers,

so I am currently planning my japan trip for autumn and I am really really unsure if I need the JR pass or not (I know about the price hike and would book before)

So I was wondering is there any App or Website I can use to best see my options and train prices?

For example I would love to do some day trips from tokyo.

Like Tokyo > Hakone, Maybe Tokyo > Kamakura

I want to go Tokyo > Kyoto and stay there either for some days (2-3) or even more (5-6) and then do day trips from Kyoto too like: Kyoto > Osaka, Kyoto > Himeji

I am not sure I can do all of this with the JR Pass ? I also find it widely hard to understand how to actually book and reserve all these trains with the Pass.

Any help would be greatly appreciated!

best,
Ichii

How To calculate Train Fare :
Millions of Foreigners every day use hyperdia

Hyperdia has been seriously nerfed for the past couple of years because JR started charging for timetables.
Personally I use https://japantravel.navitime.com/en/area/jp/route/ It is pretty accurate, but the timetables are a little out of date meaning occasionally trains are a few minutes different and it defaults to non-reserved seating.
For the travel outlined in the OP, other than a round trip Tokyo to Kyoto the other trips are pretty short/trivial and you would struggle to make much saving on a 7-day pass and the 14-day pass would be a lot more expensive. You simply are not travelling far enough in a short space of time to make it pay off.