There are 3 major zones of food stalls in Hakata - near Nakasu (the red light district of Hakata), near Tenjin, and near Nagahama. I went to the ones near Tenjin.
If you do decide to go to the food stalls, find one that's fairly busy. Find one that is clearly following the laws: (1) the menu should be clearly visible, and (2) no raw food is allowed to be served as a main dish (so no salads, sashimi, etc). Even if the menu is in Japanese, as long as you find a good stall you should be OK - the locals will be more than happy to help you chose what looks good.
These food stalls in Tenjin are very easy to find, since they are in front of major department stores. I ended up going to the same stall for two straight nights since the regulars were really kind and the food was fantastic.
Naka-chan, in front of Hakata Takashimaya
The stall is surrounded on three sides with benches, so while making room for other customers, I ended up being surrounded by the locals. They gave me a lot of advice, such as that Naka-chan has large portions (so always ask for a half serving) and which dishes are yummy. And yes, I had my fill of shochu!
Mentaiko and egg
Fishballs and other surimi products are originally from Kyushu. The locals especially urged me to try "Gyoza-maki" (yep, a gyoza wrapped in surimi)
Being seated near locals meant that they shared their dishes with me. Yum yum!
Horumon Yaki (stir fried pork intestines)
Yamaimo Teppan yaki
Ground Yamaimo grilled like a pancake, similar but fluffier than an okonomiyaki
A view inside Naka-chan's counter
I thought it hilarious to see a huge neon sign for "Ukon no Chikara" ("the power of cumin"). This drink is said to relieve hangovers - how fitting to put a neon sign right near the bars!
All of the major areas of Hakata are quite close to each other - I could walk from my hotel to Tenjin, passing through Nakasu. Here is a view of the Nakasu food stalls.
Hakata is also famous for pork bone soup ramen. It surprises me that most Westerners now consider pork bone soup to be the only soup for ramen - it was not that popular in Japan until a few years ago. Ippudo, which also has stores in the US, started in Hakata.
And yes, I went to Ramen Stadium in Canal City (a shopping center) to eat my ramen.
The ramen was yummy, but honestly, I can get good pork bone soup ramen in Kobe now. On the other hand, I had a blast at the food stalls!!
I'm finally done with my trip to Hakata. Hope you enjoyed my trip as much as I did!