Hi,
The JR Pass is of very limited value in Osaka, Kyoto and Nara. For Osaka you can use it on the Loop Line, which takes you to some interesting places, and for Kyoto you can use JR to go to Arashiyama (the western area). Nara is far less developed, and Kintetsu trains might serve you better. You cannot use the JR Pass on city subways or non-JR buses.
In cherry blossoms season, there are many popular places you can go to, and you can expect a lot of other people to be there as well. These sites have more info:
http://www.japan-guide.com/e/e3951.html
http://www.japan-guide.com/e/e4117.html
http://www.japan-guide.com/e/e4018.html
The best place of all though is Mt. Yoshino in Nara, but it's a mountain climb your parents might not have the stamina for:
http://www.japan-guide.com/e/e4152.html
For access to the Fuji 5 Lakes & Kawaguchiko, see:
http://www.japan-guide.com/e/e6905.html
http://www.japan-guide.com/e/e6906.html
For Nara, many of the best sites are around Nara Park, which is about a 20 minute walk from the JR Nara Station. If your parents are very frail, a taxi is better. In the park be sure to buy some crackers (called senbei, about 150 yen for 10) to feed the deer. They've been trained to bow to you if you do it to them, and more than a few are a bit more than friendly when they see you have food. Near the park are also 2 nice traditional gardens (Isuien & Yoshikien; the latter is free for foreigners) you should see - most tourists just stampede past it without noticing them, so they are not so crowded.
https://www.youtube.com/watch?v=kk-7IoLELio
http://www.japan-guide.com/e/e2165.html
Himeji would be a SUPERB day trip - they are just finishing multi-year renovations and it looks spectacular. Be sure to see the Kokoen gardens next to it as well. Again, most tourists just blow past and never see them.
For Tokyo, some of the best places are: Yoyogi Park, Nakameguro, Ueno Park, and Shinjuku Gyoen. Expect massive crowds though.
http://www.japan-guide.com/e/e3050.html
Enjoy.