There are several areas where people usually go when they want to enjoy nice views on the Fujisan in a ryokan...
1/ Hakone : this is really the most famous spot, with a lake, lots of ryokan and great views on the mountain is the weather is clear.
2/ Fuji Five Lakes : an area north of Fujisan where many ryokan are located
3/ Izu peninsula : little further from the mountain, views are less impressive, but the peninsula offers many interesting attractions...
Recommending one specific ryokan is quite difficult, especially if you don't give any information on the budget. In an upper class accommodation, you can expect great food, but you will have to pay for it...
Here is a short list of ryokan available in Hakone, for example :
http://www.japaneseguesthouses.com/db/hakone