There are numerous smaller islands off the coast of Kyushu as well, usually part of the prefecture they are closest to. However there are some that are further away, such as the Amami Islands that are part of Kagoshima Prefecture, as well as Tsushima, which is part of Nagasaki Prefecture.
Kyushu is home to some peculiar dialects of Japanese that speakers of standard Japanese find difficult to comprehend, particularly the Kagoshima dialect which is completely unintelligible to outsiders. However, all people are able to speak standard Japanese and especially in the cities younger people may also have a limited command of English.
Fukuoka is Japan's busiest international hub after the trio of Tokyo, Chubu and Kansai and has excellent connections throughout Asia and Japan. All the other prefectural capitals also offer limited service within Japan (mostly to Tokyo) and to a few major Asian cities (typically Seoul and Shanghai).
The Sanyo Shinkansen line runs from Shin-Osaka to Hakata Stn (Fukuoka) and some trains continue along the Kyushu Shinkansen line to Kagoshima. All shinkensen trains stop at Kokura Station in Kitakyushu and Hakata Station in Fukuoka; a trip by train all the way from Tokyo to Hakata takes 5 hours by Nozomi train without any transfers and costs ¥22,220 (adult, unreserved seat). There are no Hikari trains that go the full distance from Tokyo to Hakata, so with the JR Pass, you'll need to change trains to a Sakura train in Shin-Osaka or Okayama, adding 45-60 minutes to the trip. Given the time it takes and cheap foreign tourist airfares from ANA's Experience Japan Fare and JAL's Explorer Fare, as well as low cost carriers like Jet Star and Peach, flying usually makes more sense for such long distances. You can also go from Kyoto to Hakata with the JR Sanyo Sanin Area Pass, JR Setouchi Area Pass, as well as down to places in northern Kyushu (Kumamoto, Nagasaki, Aso, Beppu et. al.) on the JR Sanyo Sanin Northern Kyushu Pass. Be aware however that between Kyoto and Osaka is not part of the Sanyo Shinkansen line, so with JR West passes, those starting in Kyoto need to take a limited express train (Thunderbird, Haruka, or Super Hakuto) or a rapid train to Shin-Osaka and then catch the bullet train. No matter what, avoid all the Kodama shinkansen trains which stop at every single bullet train station.
The Kyushu Shinkansen crosses the west side of the island to Kagoshima in the south. Many trains to Kagoshima start in Osaka, and the full course takes about 3¾ hours by Mizuho and ¥21,780 (adult, unreserved seat). The JR pass is not accepted on Mizuho trains, but they are accepted on Sakura trains which make the journey in 4¼ hours.
The Hakata to Kagoshima run takes about 75-95 minutes. There are also good limited express trains servicing most anywhere of interest on the island, so you can take a train from Hakata to just about anywhere else of interest on the island in less than 2 hours; the exception being Miyazaki which is about 3½-4 hours from Hakata.
Willer Express  is a company which provides daily night time bus services from Nagoya, Tokyo, and Osaka to Kyushu. They offer an online booking services in Japanese, English & Korean.
The train is the transport mode of choice on Kyushu, and JR is by far the dominant rail network on the island. The Kyushu Shinkansen zips across from Fukuoka (Hakata Stn.) via Kumamoto to Kagoshima in 75-95 minutes, and there is a fairly rapid limited express network to get almost anywhere else. There are also some scenic local train lines such as the JR Hisatsu Line (肥薩線) from Kumamoto via Yatsushiro to Kagoshima which are considered one of the most scenic in Japan, and there are comfortable, sightseeing oriented, trains on these lines, plus some runs with unique roll stock, most notably the Aso Boy from Kumamoto to Mt. Aso and the Steam Locomotive Hitoyoshi from Kumamoto to Hitoyoshi, along the Hisatsu Line. A few non-JR lines, like the Nishitetsu train between Omuta and Tenjin in Fukuoka may offer more convenient travel to some destinations like Dazaifu, and there are a few short rail lines like Matsuura Tetsudo and Minamiaso Tetsudo that run through some fringe and isolated areas, however service is infrequent and a rental car may work better.
The JR Kyushu Rail Pass , offers unlimited travel on JR Kyushu's lines, including the Kyushu Shinkansen but not the Sanyo Shinkansen between Hakata and Kokura, nor any JR Kyushu highway buses. The JR Kyushu Rail Pass may only be used if you are in Japan with a "temporary visitor" status, except for the Ryugakusei Pass (see below). There are five types of Kyushu Rail Pass: the full pass which covers the entire island for 3, 5, or 7 consecutive days, one for the Northern Kyushu Area (all JR lines including and north of Misumi and the Hohi Main Line between Kumamoto City and Oita City) for 3 or 5 consecutive days, one for the Southern Kyushu area south of the Hohi Line (not valid north of Kumamoto and Nobeoka) for 3 conseuctive days, the Fukuoka Wide Pass for 2 consecutive days that covers from Omuta to Fukuoka City, Kitakyushu, or Yukuhashi, up to Shimonoseki in Yamaguchi, and Karatsu in Saga (NB: the city subway is not covered, and any limited express train seating is unreserved only). The last version is the Ryugakusei Pasu which is for foreign exchange students living in Japan (unreserved seating only). Multiple purchases of the passes are allowed as long as the times do not overlap.
The prices of the passes are as follows:
All Kyushu Area
Northern Kyushu Area
Southern Kyushu Area
Fukuoka Wide Pass
Buses serve those parts of Kyushu outside the railway network, but schedules tend to be very limited. There is also the Sun-Q Bus Pass for 3-4 days unlimited bus travel : 4-day All Kyushu Pass is ¥14,000; 3-day All Kyushu Pass ¥11,000; 3-day Northern Kyushu Pass ¥9,000, and 3-day Southern Kyushu Pass for ¥8,000. It should also be noted that there are some popular areas in Japan, such as Takachiho in Miyazaki, as well as Kurokawa in Kumamoto that have no rail access at all.
Kyushu has numerous places that have infrequent, inconvenient, or even no public transportation at all, and many are among the island's best. For some itineraries, renting a car makes the most sense for those who are up to it. It may be better to use the train or bus for the long distance legs, and rent a car for some day use trips. For those in groups of 2-5 however, using a car to travel the whole island might be the better choice, and there is a Kyushu Expressway Pass that might serve you well. Fuel can be pricey however, and parking may be troublesome in bigger cities (though far, far better than Tokyo or Osaka.
Like the rest of Japan, Kyushu has no shortage of mountains, and there is tons of great hiking. Some notable areas are Mt. Hiko in Fukuoka, the Kuju Mountains, Kirishima-Kinkowan National Park, Aso-Kuju National Park in Kumamoto, Kaimondake and Sakurajima (periphery only) in Kagoshima, Mt. Unzen in Nagasaki, Mt. Sobo, and Mt. Yufu near Yufuin in Oita. There are some great hikes around Kyushu called Olle Hiking. The length varies between 10-15 km as well as the difficulty.
Each prefecture has its own specialty food they are proud of. In Fukuoka, they are very proud of their tonkotsu (thick pork broth) ramen and mentaiko (spiced cod roe). In Nagasaki, Chinese influenced dishes like its thick chanpon noodle soup with squid, fishcake, octopus, etc, as well as saraudon (thin Chinese noodles topped with shrimp, squid, cabbage etc) are exquisite and very popular. In Kagoshima, its kurobuta (from Berkshire pigs) pork is very famous, and so on. Try something new.
Kyushu is the home of shōchū (焼酎), the fiery Japanese distilled liquor. It's typically around 25%, but some varieties can be much stronger. It can be distilled from nearly anything including rice, barley, brown sugar and buckwheat, but Kyushu is best known for potato shōchū (芋焼酎 imojōchū), particularly that from the ancient province of Satsuma (modern-day Kagoshima). See also "Japanese sake tourism#Shochu and Awamori distilleries" article.