If you want a room with private ensuite outdoor onsen and a view of mtfuji, then kawaguchiko has many (eg, Konanso). But the onsen water quality is subpar in kawaguchiko and Fuji lakes area in general imo.

in hakone, the Asian suite room at hakone green plaza has great private tub that looks out towards mtfuji. The onsen quality is great and prices reasonable. Drawback is that the place is more of a hotel and the food doesn’t blow you away although still tasty.