Ichiran is one of the largest chains of Hakata ramen restaurants, with locations all across Japan and in several other countries. At this factory, you can learn about the ramen-making process and view their factory where they make noodles. At the end is a small restaurant with a weekly special dish. The museum is entirely in Japanese.
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能古島
A small (about 12 km around) island in the middle of Hakata Bay and offers some splendid hiking, swimming, and camping. It is easily reached by a 10-minute ferry ride from the Meinohama Port. The ferry departs every hour usually at 15 minutes past the hour from 05:15 in the morning to 23:00 at night, with service every half hour during the morning and evening rush (07:15-08:15 and 17:15-18:45).
愛宕神社
A hidden gem near the Muromi Subway Station, with a superb view of the city and Hakata Bay from a hilltop. You can also see many storks that fly by and nest in the area. Walk west from the subway station across the Muromi Bridge until you see the Atago torii gate with the stairs heading up. Alternatively there is a side road you can walk up if you don't like stairs.
福岡タワー
The triangular reflective tower has magnificent views of the city and Hakata Bay from its 123-meter-high observation deck. (The whole tower is 234 m; the remaining 111 m is a television mast.) In Christmas and the Star Festival (Tanabata) on July 7, this tower is decorated. During the rest of the year the view is best at night time. This is an iconic symbol of Fukuoka. There is a restaurant which commands a ¥300 sitting fee in addition to the meal. The menu is limited and the food is mediocre at best.
福岡市科学館
Cotains Robosquare on its 5th floor. You can see and play with different kinds of robots and watch some of the engineers at work. Despite the imposing sounding name, Robosquare is one medium sized-room with a few robotics exhibits and some toy robots and is primarily aimed at children. Some English explanations are now available.
A stretch of beach where visitors can enjoy a bit of swimming and sun. While the water isn't as clean as the waters further west and east in Fukuoka, you can still take a refreshing dip. There are a few lovely patio restaurants and bars which are an ideal location to watch the sun set. The area behind the Seahawk Hotel is good. It's less crowded during the summer.
福岡市博物館
Permanent exhibition of city history and changing temporary exhibitions.