Hakone or Five Lakes for Mount Fuji (Views)

Hi all,
on my first trip to Japan (at the end of october) I'd like to enjoy the view of mount Fuji. For that Ifd like to spend one night in a ryokan with onsen either in the Five Lakes Region or in Hakone whilst travelling from Tokyo to Kyoto.
I have no idea which place is better – better views, more interesting things to do, better to get there from Tokio and then leaving to Kyoto
Do you have any suggestion which place I should choose and maybe a recommendation for a ryokan (if it is a really nice place up to Y 25.000 per night for a room with private bathroom).
Thanks a lot

For things to do. Use this website and check what appeals to you.

If views of Fuji-san are the main reason for selecting location, then Five Lakes has a better chance of seeing mount Fuji than Hakone.

Hakone has better access since Odawara has a Shinkansen station. But nothing an extra bus trip cannot fix to get to Five Lakes.