Oh and one last thing, if you have booked your hotels or at least have some idea where you want to stay in Tokyo and Osaka use the specific station names. Tokyo and Osaka are specific stations which may or may not be convenient to where you are staying. If you're actually staying near Namba (vs. Nankai Namba and JR Namba) the route to a particular location might be different than from Osaka. The same holds true for Tokyo. The shinkansen only goes to certain stations. Staying near Tokyo Station or Shinagawa Station in Tokyo is fine and there are lot of hotel choices, restaurants, cafes and shopping. Shin-Osaka is sort of... dull... it's mostly business hotels with small rooms and lots of convenience stores. It's not unsafe, but it's not somewhere I would ever pick to stay again.
Hyperdia also doesn't know about stop overs. I have personally never done this, but people on this forum have. So you could buy a ticket between Tokyo and your destination in Osaka and then have a stop over in Odawara (where if you go to Hakone you need to pay for private lines no matter what as JR only goes as far as Odawara) or have a stop over in Atami or Mishima (if you were to go to Shuzenji, just to give some other onsen destinations) This page gives a good explanation and explains how it works:https://travel.stackexchange.com/questions/66616/when-are-stopovers-pe...
You will not save a ton of money, but you will save something vs. buying two separate tickets, but this is only important if you decide to stop off someplace on the Tokkaido line (Hakone, Atami, Mishima) to experience an onsen. If you go to Arima outside of Kobe, then you would either pay out of pocket or get as far as you can on your JR West Pass before needing to use a private line.
It will take a little longer, but you can also technically fly between Haneda and Itami airports. A lot of people who live in Japan do this because it tends to be cheaper. You also up your chances of a spectacular Mt. Fuji view. You must fly into Itami thought, KIX flights go further south.
Osaka Station to Kyoto Station is 570 yen by Special Rapid (a type of local train) and takes 29 minutes. They run every 15 minutes. With a JR West pass you could shave off 2 minutes from that time to 27 minutes if you catch a limited express which would cost 1230 yen without a reserved seat, or is covered by most JR West or the full JR Pass.
Even with a full JR Pass it is on average 32 minutes from Osaka Station to Kyoto Station via Hikari or Kodama shinkansen. Hyperdia is also giving a lot of 3-4 minute transfers in Shin-Osaka. I admit, I have done 3-4 minute transfers in Shin-Osaka Station, but I don't know if you will want to. I think it is harder in the shinkansen direction because it's all up stairs vs. down stairs.
When using Hyperdia and wanting to get some ideas for a full JR pass, make sure to go to "More Options" and click the exclude Nozomi button. Full JR Passes can not be used on Nozomi and Mizuho. They can be used on Hayabusas, but unless you are planning a trip from Tokyo to the north, it won't matter. If you get a JR West Pass, outside of the 1 day, you can take Nozomi and Mizuho between Shin-Osaka and whichever station is your destination station within the pass, like Himeji or Hiroshima.