There isn't really the option to break up a journey and stop along the way without buying multiple tickets.
However if you want to travel like this, perhaps a JR Pass would be a good option for you, as it allows unlimited JR train travel within a 7, 14 or 21-day period.
You can't take the Nozomi train with the JR Pass, but you can take the other trains that run along the same route (for example the Hikari and Kodama trains).
You are talking about making stopovers. The pass is one easy way to do this. With a regular fare ticket, it is possible to do so as well, depending on the distance that you are traveling (and backtracking is not allowed). It does take some reading and understanding of how JR works though. If you want more info, you can read: http://paulstravelpics.blogspot.com/2017/06/advanced-japan-how-to-hop-on-hop-off-jr.html
Comments
There isn't really the option to break up a journey and stop along the way without buying multiple tickets.
However if you want to travel like this, perhaps a JR Pass would be a good option for you, as it allows unlimited JR train travel within a 7, 14 or 21-day period.
You can't take the Nozomi train with the JR Pass, but you can take the other trains that run along the same route (for example the Hikari and Kodama trains).
https://www.japan-rail-pass.com/jr-pass
Hope that helps!
Japan Experience
It does take some reading and understanding of how JR works though. If you want more info, you can read:
http://paulstravelpics.blogspot.com/2017/06/advanced-japan-how-to-hop-on-hop-off-jr.html
https://travel.stackexchange.com/questions/66616/when-are-stopovers-permitted-on-japan-railways-jr-trains/66617
http://www.japan-guide.com/forum/quereadisplay.html?0+152139