From Hiroshima, consider day trips to Onomichi and Itsukushima (Miyajima).
I don't see anything wrong with any of your ideas - Himeji, Kyoto, Nagasaki are all great. In terms of convenience of connections, Nagasaki is quite a haul from the city. Hiroshima airport is also a long bus ride from the city. The city with the best located airport is Fukuoka. Might be a good place to consider for the end of your trip if you don't already know it.