Hi,
A 7 day JR Pass would easily pay off for your plans; you should activate it just before starting your trip down to Kyoto and beyond. If your first day on the pass is the 25th, your last day would be April 1st. Since you are spending quite a long period in the Tokyo area, some day trips from there would also be a good idea. Nikko, Kamakura/Enoshima, and Hakone are the most popular choices. The longest of them would be Nikko, and if you go there on April 1st you could still take advantage of the Pass and enhance its value. There are regional passes you can take advantage of for seeing Kamakura as well as Hakone. See:
http://www.japan-guide.com/e/e2358_003.html
http://www.japan-guide.com/e/e2358_004.html
http://www.japan-guide.com/e/e2358_008.html
For Kyoto, be sure to take at least half a day and see Nara as well. When the temples/shrines close around 5PM, you can easily zip over to Osaka and enjoy the night life there. Dotonbori is a must see place. And the views from the Umeda Sky Bldg and Abeno Harukas Bldg are spectacular.
https://www.youtube.com/watch?v=COJ_MeXbeow
https://www.youtube.com/watch?v=xb1wuyAGgyQ
https://www.youtube.com/watch?v=-AyUZmGbW8g
For Hiroshima, IMHO one day is enough to see Hiroshima City, and one day for Miyajima. You can use the extra day to explore nearby sites like Iwakuni, with its iconic bridge and mountaintop castle. It is also good for cherry blossoms:
https://www.youtube.com/watch?v=0COOZXi66mM
You can see it in a few hours. You can also spend some time in Okayama, which has one of Japan's most famous historical gardens, Korakuen, as well as a lovely and almost unknown garden, Handayama:
https://www.youtube.com/watch?v=5zAI3_N7NEM
https://www.youtube.com/watch?v=JGQ8o7k9GbA
Or if you prefer, there is the beautiful Kotohira in Kagawa, Shikoku. It's famous for its shrine and mountaintop view, but it is the climb up that is the real adventure:
https://www.youtube.com/watch?v=ley9rVIewoQ
Another choice is the little known city of Onomichi. It has a hillside temple tour you can take; but its real treasure is an almost unknown temple on one of its small islands - in fact it's been thought of as almost a Buddhist Disneyland:
https://www.youtube.com/watch?v=97Q5EjEOXI8
Regarding a hotel, you are going to Japan at the height of cherry blossom season - which is extremely beautiful, but also a lot more crowded. You may find trouble in getting a place; at least a moderately priced place. This info can help:
http://www.japan-guide.com/news/0029.html
A few cheaper business hotel chains you might look at are:
http://www.toyoko-inn.com/eng/
http://www.superhoteljapan.com/en/
http://www.route-inn.co.jp/english/
http://www.richmondhotel.jp/
I also recommend you spend a night in a Japanese Inn (ryokan) at least one night for the experience. Some inexpensive places are listed below:
http://www.ryokan.or.jp/english/
http://www2.dango.ne.jp/kimi/ryokan.html
http://www.tamaryokan.com
http://www.tokyoryokan.com
I am sure you can find a lot of good memories in your coming trip.