14 days in Japan

I finally booked my trip to Japan upcoming February and this is what my planning looks like:
day1: arrive at KIX, osaka (full day)
day2: osaka (full day)
day3: hiroshima (half day) + miyajima (half day)
day4: miyajima (leave in morning) + himeji (half day) and go to kyoto
day5: kyoto (full day)
day6: kyoto (full day)
day7: nara(full day)
day8: kyoto (full day)
day9: tokyo (full day)
day10: tokyo (full day)
day11: kamakura (full day)
day12: tokyo (full day)
day13:back to osaka(full day)
day14: fly back

I know osaka and kyoto can be visited from each other really easily but I prefer to stay at both cities :)
Does this seem like a do-able plan? I don't have the full details worked out yet of my trip, only the major trips.

That looks very doable, though don't forget to allow for your travel times. To do a full day in Hiroshima/Miyajima, you'll need to leave Osaka around 7:30am. Likewise, your first day in Tokyo won't be a full day once you allow for travel from Kyoto (unless you're leaving very early in the morning).

The itinerary overall doesn't look bad at all, although you're putting in more than enough time for Osaka, and your Day 13 you could go back and see Kobe for a day.
You can do both Hiroshima City and Miyajima in a day with an early start, and for that part of the trip you might look into getting a JR Kansai Hiroshima Area Pass.
http://www.japan-guide.com/e/e2361_kansai_hiroshima.html
You can take a Nozomi train with it and get down there quickly, and the next morning if you feel like it you can expand your trip a bit more by seeing Iwakuni for a few hours with its iconic bridge.
https://www.youtube.com/watch?v=0COOZXi66mM
For Miyajima, the big 3 activities are seeing the Itsukushima Shrine, Daishoin Temple, and Mt. Misen - but if you're limited for time, definitely see the first two which are done quicker.
https://www.youtube.com/playlist?list=PL7LcPcmoSg-iCNZ6AdsKGUB-HPKNxP1...
If you rearrange your plans a bit and use the pass to go see Nara as well, you will save even more. The Todaiji Temple is an absolute must.
https://www.youtube.com/watch?v=wiGqHkHIPWs
The Isuien Garden is also an overlooked gem.
https://www.youtube.com/watch?v=kk-7IoLELio
For your Days 8-14, you can use a 7 day JR Pass, and for Day 11 if you are going to put in a full day for Kamakura, you can also include Enoshima. You might even fit in a bit of Yokohama if you like; the Chinatown is famous and Sankeien is gorgeous.