Two days between Kyoto and Hakone

I am going to Japan for 2 weeks in November and have two days open in the itinerary that I am trying to figure out. Our schedule is as follows:

Nov 9 - Land in Tokyo
Nov 10-13 Kyoto (wedding on Nov 11 so this is not flexible)
Nov 13-15 two nights OPEN
Nov 15-16 Ryokan in Hakone
Nov 16-18 Shimoda
Nov 18-22 Tokyo

We were thinking about going to Takayama for 2 days but I am worried we will be wasting a lot of time with travel. I was also thinking about staying in Kobe or Osaka but I wasn't sure if there was enough to do for two days?

Are there any other places near or in between Kyoto/Hakone that would be worth a stop? I am open to two different places as well (e.g. one night Osaka one night somewhere else) as long as travel between the two is not very long.

I am travelling with my boyfriend (both ~30 years old) and we love nightlife/good food but are also open to a trip more in the country side. Coming from Kyoto where we will see a lot of temples/shrines I don't want that to be the focus of the two open days. Thanks!

My answer to everything is always Nara. And stay in the old section of Nara Hotel.

But then if the 2 days fall on the weekend consider Kiso Valley (Magome is a lot of fun on the weekend, but quiet during the week, Narai is similar). Kiso Fukushima is a good base for that.

If you would like to be near the water, consider the Izu peninsula which is very handy to Hakone. We stayed at Ajiro in a ryokan called Taiseikan which was fantastic. The town is deadly quiet but it is a short walk to the train station, Atami is 5 minutes one was and Ito isnt far the other, Ito is quite pretty and the zoo there is fantastic. Also Shuzenji is nice, apparently very nice in autumn.