Here's a nice travel itinerary for you: Shinkansen from Hiroshima to Hakata, party it up in Hakata Saturday night, enjoy some pre-dawn Ramen in the warmth and friendly conversation of the yatai, and catch the first limited express to Nagasaki.
Of course, if you happen to meet someone friendly in Fukuoka... well, Nagasaki might be put on hold. In any case, once you're in Fukuoka, it's a fairly good staging point to travel across the rest of Kyushu - limited express trains to Nagasaki run every half hour or so for about ¥5000. However, after visiting Nagasaki, I'd really recommend sticking around Fukuoka for the day instead; it's a much better city in terms of attractions, atmosphere, people, and nightlife.
Not that Nagasaki doesn't have its perks. Trains run in one direction as the city is located on a pennisula in Kyushu, but the trams do a good job taking you the many kilometers of the city. Of course you have the international attractions like the 2nd Peace Park to honor those fallen during the atomic bombing on August 9th, 1945 (11:02 AM); not quite as large as Hiroshima's, but equipped with more art, creating a more introspective environment than you might see with the A-Bomb dome.
In addition, Mount Inasa offers an excellent view of the city at night, the skyline a mere twinkling of lights from the height of the observation tower. The ropeway runs until 9 PM, and a roundtrip ticket will cost you ¥1200. Of course, you can climb the mountain, but I wouldn't recommend it for a vacation plan.
But perhaps the most impressive aspect of Nagasaki is its rich diverse history, practically unprecedented when you consider the rest of Japan. A few hundred years ago, when all of Japan's harbors were closed to trading, Nagasaki's was the only one that remained alive and well. As such, the city developed a large foreigner presence, particularly among Chinese and Dutch traders. To this day you can see the Dutch-style houses in an area of the city called Dejima and the Holland Slope. Nagasaki supports its own Chinatown district and supports two excellent Chinese shrines, Sofukuji and Kofukuji.
The best food? They have champon, a local noodle specialty, but I preferred the kasutera (カステラ) - a simple pound cake available in spades anywhere in the city. You can also pick them up in Hakata Station - look for a store with the Batman logo, I kid not. If you want some imported foods, there's a shop in the station shopping area similar to Jupiter Imports.