Onomichi has lots of locals living in it, but it's definitely a popular place for Japanese locals to visit. From that perspective, it's still interesting for a foreigner, but has some of the same drawbacks as the standard touristy cities.
The Kasugayama Primeval Forest behind the shrine is a peaceful place to go hiking. Although it isn't nearly as mysterious in person as 'primeval forest' sounds, it's still a great place to get away from the hustle and bustle of urban cities.
Kasuga Shrine is one of the oldest shrines in Japan and the head of the Kasuga branch of shrines. The moss covering much of the architecture is unique compared to the spotless shrines in other parts of Japan.
The local fish market has affordable, fresh sushi shops. There are also dozens of high-end sushi restaurants that people from all around Japan travel to Kanazawa to eat at.
Since Kanazawa is a popular destination for Japanese people, and foreigners tend to go to Kyoto, many of the attractions in Kanazawa are less language-friendly to English-speakers. That being side, most signs are in English, and many of the main attractions still offer pamphlets and directions in English.
Seeing the waves splash against the shrine is considered one of the Three Views of Japan. The location is also considered a UNESCO World Heritage Site.
Miyajima is a popular day-trip location from tourists in Hiroshima, so there's quite a few people walking around town during the day. However, the last boat back to Hiroshima leaves prior to sunset, so watching the famous tori gate during the sunset will be far less crowded.
The Ise Grand Shrine is unique in Japan as being the top of the hierarchy of Shinto shrines connecting to Japan's imperial house. It is taken down and completely rebuilt every 20 years.
Despite being a small town, Ise is home to the Ise lobster, which is well-known throughout Japan for its culinary applications. There are entire traditional course meals using the Ise lobster at Ise's traditional inns.
When the Polish first came to Japan through Nagasaki's ports, they brought with them their egg-based sponge cakes. 400 years later, Nagasaki has really refined their recipes, and this cake is one of the favorite desserts of Japan. Some of the historical shops still operate their flagships in Nagasaki, where the cake is exquisite and service and impeccable (change is doled out in completely new bills with consecutive numerical codes).
Nagasaki was rated as one of the best night views in all of Japan. Given its unique coastal structure, there are several great viewpoints around the city.
Since Okinawa was originally a separate country from Japan, Ishigaki is one of the best ways to explore Okinawan culture. There are unique food, phrases, and styles of dress visible all over the island.
While there is a bus and some taxis, the more efficient way to get around is by car. Renting a car will mean added costs, but it offers the most freedom to fully explore the island.
Home of tonkotsu ramen, famous chains such as Ippudo and Ichiran originated from this city. Getting off the train, you can immediately smell the thick fragrance of pork broth all around the city.
There are a lot of famous foods in Hakata: motsu nabe, tonkotsu ramen, mentaiko. While there's also a few shrines and gardens, Hakata is a fairly modern city and thus doesn't have a lot of traditional cultural attractions.
There are two main styles of ramen in Japan, Hakata and Sapporo. For ramen-lovers, a visit to Sapporo for the northern-style ramen would go hand-in-hand with a visit to Hakata.
The annual festival in February showcases hundreds of ice/snow sculptures. Some as small as a life-size pikachu, others are full-size illuminated light-show castles. Along with all the sculptures are music, food, and game events.
Since Aomori is a small coastal city, the restaurants carry an air of local pubs, where everyone knows everyone else, and they're very friendly and welcoming to foreigners.
Aomori ships the majority of the apples that get consumed around Japan, including the expensive $10+ per apple gifts that get presented in special occasions. Thus, Aomori is the prime location to try these apples at a more affordable price.