If you had to do your first Japan trip over…would Hakone still be on your list?

Hi everyone, my spouse and I, and my mother-in-law, are flying to Japan for the first time ever February 11-March 1 for 20 days.

We fly in from Puerto Rico, so we have 17 full days in Japan.

I want to know your opinion on whether or not we should split those days across Tokyo, Kyoto, and Osaka (Day trip to Nara included)

OR

if we should splurge on a 2 night stay in Hakone

I'll be clear, for us this is a MAJOR splurge. We would use points, share a room, save a lot just to do it in a financially responsible way. We are by no means the type of people who comfortably spend even $300/night at any hotel just casually (or even impulsively lol)

But it IS our first time in Japan, and it seems like a great way to add some dimmension, relaxation, and luxury to a pretty active trip.

If you had to do your first Japan trip over and you had no clue what you were getting into (like me) what would you do? Give all your days to the Golden Route, splurge at a Ryokan, or branch out?

Thank you in advance for your advice!