If you're interested in food, you really should stay more nights in a ryokan, IMHO.
Unless you're going to splurge on a kaiseki restaurant, you won't get the sort of food experience that you have in a ryokan (and, in any case, the whole combo of baths, yukata, total relaxation, and awesome food isn't on offer in restaurants).
For my money, I'd try to stay in ryokans in countryside areas, rather than city ones (as the baths and views are generally better - plus you get more variety of local food. Sansai, ayu, etc). Plus, there are loads of food options in cities, so you may well want to eat out.
3 nights in Takayama (even with a trip to Shirakawa) is quite a lot. You could fit a trip to the Oku-Hida region for one night in a great ryokan, for instance. you'd probably spend less/the same as on a ryokan in Miyajima (generally quite pricy because it's such a popular place). I've stayed in one of the nicer/more expensive places in Miyajima and it was average-to-good, but not spectacular for what it cost.
I'd also try to fit at least one night in a minshuku, for food that's still unique, but is a bit more homestyle. You could do that in Kanazawa, for example (and Kanazawa food is awesome! You MUST have lunch in Omicho market if you like seafood.)
You could also overnight in Shirakawa en route from Takayama to Kanazawa. Staying in a gassho-zukuri, especially one where they cook over an irori, is a great experience, and the food is homestyle but worthwhile.
We (love onsen and) have a big interest in Japanese food. On a 23-day trip, I'd be looking to stay in a ryokan 4 or 5 times. The kaiseki meals are the ones I remember most from all our trips, and are the ones that you just can't get in my home country (even if paying extortionate prices).
We typically stay in cheap business hotels/minshuku for most nights, and then fit in a ryokan stay every 3-5 days. Also, maybe try to get a mix of maybe one really special ryokan, a couple of mid-priced ones, and a cheaper one. This will give you a feel for the subtle differences in quality of the simpler food items (e.g. really good nori, or really good tofu). When a ryokan does really good food, it's not just that it cooks with more expensive ingredients, it's that it takes lots of care with ALL it's ingredients.
N.B. I'd recommend NOT to stay two nights in the same ryokan (in order to get more variety of food), even if you're staying in the same area.
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