The first thing that pops up is that you are keen to see the cherry blossoms, but for some things your dates are fixed, so that could be a problem. Preliminary forecasts say that this year the blooming will be following the average of bloom times, but of course nature sometimes throws a curve ball. You should take a look at the various popular places as well as when they come out.
http://www.japan-guide.com/e/e2011_when.htmlhttp://www.japan-guide.com/e/e2011.htmlYou should also check out these forecast sites from time to time in February & March.
http://sakura.weathermap.jp/
http://www.jnto.go.jp/sakura/eng/index.phphttp://www.rurubu.com/season/spring/sakura/You should be able to see some blossoms somewhere, even going further north to Sendai or somewhere at the end of your trip. I would suggest you don't just stop there though. The shibazakura are worth seeing as well.
http://www.japan-guide.com/e/e6919.htmlAnd since you will be in Japan at the end of April, you have a chance to see the wisteria, which are just breathtaking. The best place to see it in your area is the Ashikaga Flower Park, and while the crowds will begin to swell with the start of Golden Week (a major holiday period), it is still absolutely worth it.
https://goo.gl/EvSI3vThe Hitachi Seaside Park is another gem you two would likely love.
http://en.hitachikaihin.jp/As to anything missing, your itinerary looks pretty packed, but if you want alternatives, you should absolutely include Nara, and if you can, Himeji is very good as well. Miyajima is also a good choice, and while accommodations there are higher, there are some good Japanese inns (ryokan) there you should try at least once for the experience. Once the day trippers leave, the whole area gets very peaceful.
https://www.youtube.com/playlist?list=PL7LcPcmoSg-iCNZ6AdsKGUB-HPKNxP1...Also just a bit beyond Miyajima is Iwakuni and it is also a secret cherry blossom gem.
https://www.youtube.com/watch?v=0COOZXi66mMI do hope you realize that to go from Osaka to Takayama takes about 4 hours on trains, and it would be 2 more hours to go to Kanazawa. I suggest you stay in Shirakawago overnight at a farmhouse - you would probably find it a memorable experience.
http://www.japan-guide.com/e/e5950.htmlFor Hakone & the Fuji 5 Lakes, look at one of the Odakyu passes.
http://www.odakyu.jp/english/deels/You can also find some good ryokan in the area.
www.ryokan.or.jp/
www.japaneseinngroup.com/
www.japaneseguesthouses.com/
http://selected-ryokan.com/ryokan
https://www.tsunagujapan.com/10-tokyos-accommodations-to-experience-ja...Also since it is your honeymoon, try to stay at some love hotels. They are not expensive, they are generally large sized, and each one has its own theme and a great place to make some memories.
http://www.japan-guide.com/e/e2031.htmlhttps://www.tsunagujapan.com/10-phenomenal-luxury-love-hotels-in-tokyo...Finally look at the various rail passes and see which one suits your final plans best:
http://www.japan-guide.com/e/e2357.htmlYou can see regular fares, routes and schedules on Hyperdia.
http://www.hyperdia.comUnder "More Options", be sure to uncheck the Nozomi box since you can't ride that train using the pass.
