This gallery hosts temporary exhibitions from Kyushu and all around Asia. It has a good shop.
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Hakata-za
An experience worth checking out. Check times and prices at the Hakata-za near Nakasu. If you don't want to stay for the whole show, or don't have so much money to spend, you can watch part of a show for about ¥800; see here for details. Half price student/young (~25) adult tickets may be available day of performance to be released 20 minutes prior to the show; see here for details.
This area is next to Tenjin and is Fukuoka's red-light district, with over 3500 restaurants, as well as ramen stalls (yatai), shopping, pubs, hostess bars, rooftop beer gardens in summer, one surviving movie theater, and sex trade. The neon lights on the Naka River are famous with over 60,000 visitors a day, and it has the busiest street in Kyushu.
The 8th-century Kushida Shrine is starting point for the annual Gion-Yamakasa Festival.
The ACROS building has a terraced roof that merges with the park and contains some 35,000 plants representing 76 species. It is 809 steps to the top. Just east of ACROS is the former Prefectural Guest House, featuring turn-of-the-century architecture.
博多町屋ふるさと館
gives you a glimpse of the Hakata way of life.