Actually, a month in Kansai it too short!
But I'd say that 2 days in Nara are enough, and 1 day and some evenings in Osaka are plenty. After the temples of Kyoto close down around 5PM, you can zip over to Osaka for the evening. At night the city comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg, and Abeno Harukas Bldg are wonderful.
In addition, there are other numerous great places you can visit in the area. Okayama is not far and it is famous for its castle, plus Korakuen, one of Japan's Top 3, and also the Handayama Garden. If you'd like to get off the beaten trail for a while, the half day hike up to Konpirasan in Kotohira is stunning. Going to Takamatsu is also nice - it has one of Japan's finest gardens also, called Ritsurin.
Hiroshima also has a number of good places. Miyajima is the most famous, and aside from Hiroshima itself, Onomichi with its temple tour and Kosanji Temple is spectacular. Just beyond Miyajima also lies Iwakuni with its historical bridge and castle on top of the mountain. Taikodani is also a beautiful shrine in Tsuwano, Shimane.
Hagi Castle was actually delightful, and the preserved samurai district and Mori related temples a rarity. One of the very best is the Akiyoshi Limestone Cave, a 300 million year old wonder with huge caverns and underground river running through it.
If you can, try to find a little time to see the Japanese themselves. Go visit a Japanese supermarket and see what people typically eat. Nishiki Market is one place in Kyoto, but it's also overrun with the tourists - see the ordinary things as well and you will learn a lot. Look through a park and watch the Japanese kids play. Learn about the history of some of the places you visit before your departure - it will give your trip so much more meaning.
All in all, a lot more to explore and enjoy.