22 day Autumn Japan trip – itinerary

My boyfriend and I (young couple, first time in Japan) are traveling late September, landing at Osaka KIX and departing from Tokyo NRT.  We are interested in the culture, the food and also the nature of Japan. We look for variety and unique experiences, and a balance between crowds and quiet. So far, we came up with this itinerary:

Place Nights Plans
Osaka 4 Dotonbori & Kuromon; Osaka Castle; day trips to Nara & Kobe
Hiroshima 3 Peace Memorial Park, Museum; Shukkeien Garden; day trip to Miyajima
Nagasaki 3 Glover Garden, Oura Cathedral, Dejima; Mount Inasa views, Chinatown, Suwa Shrine
Kyoto 5 Fushimi Inari, Kinkaku-ji, Ginkaku-ji, Nanzen-ji, Uji day trip
Hakone-Yumoto 2 Reverse Hakone Loop (ropeway, pirate ship, Owakudani, Lake Ashi)
Tokyo 6 Shibuya, Akibahara, a day trip to Yokohama, Disneyland day

My question is, is this doable? Do you think it is worth it to travel to Nagasaki? I think we'll use the 7 day Sanyo Sanin Northern Kyushu Pass.

We're fit but want a semi-relaxed pace—not a rushed "see everything, experience nothing" trip. I did some research, and I think as long as we are OK with not seeing every sight and accept missing out on something, we should be ok. Thank you for all your suggestions.

by KateInHerCraftyEra