One of my favourite places in Fukuoka City is Ohori Park. It is right in the middle of the city and such a relief for many people who get tired of being surrounded by skyscrapers. It is a sanctuary for birds and other animals, too. You can just walk around the park or enjoy the swan peddler. If you want a coffee, there is Starbucks on the western side of the lake.
When I don‘t stay with my sister in the Eastern district of Fukuoka City, I normally rent a holiday apartment or stay at a cheap hotel near Ohori Park. Fukuoka City has become such a busy, noisy place. I need some breathing space.
There is Japanese Garden near the South Entrance. There is an entrance fee of 240 yen. It is closed on Monday. On every 1st and 3rd Tuesday of the month, they open Tea Room section of the building for free. You can taste Matcha tea and traditional Japanese tea ceremony sweets for 300 yen. It is small compared to those large tourist attractions in Tokyo or Kyoto, but it is just a calm and quiet place. I love it here.