There are so many exquisite ryokans in Hakone and Izu, that you must be saying none stood out because either you can't decide amongst too many great choices or you're not searching well.

Izu has a lot of great ryokans, but a lot of the best ones are only accessible by long bus rides. There are many places in train-accessible places in Izu like Ito, Ajiro and Nagaoka, but I think you'll like the atmosphere in Hakone better than those places. Hakone covers a wide area, and some places may take 1.5 hours to get to from Odawara while Hakone-Yumoto is only 15min by train. Area of Hakone with best selection of high-class ryokans that is nearest & most accessible from Odawara would be Miyanoshita / Gora area. Unless you're looking for a room with en-suite rotenburo, most places will be below your budget.