Sure, here's some information to keep in mind while planning your trip to Fukuoka, Beppu, Yufuin, and Nagasaki, Japan.

Best Time to Visit:
Overall, autumn (September to November) is considered the best season to visit these cities because of the comfortable weather and beautiful autumn colors. Spring (March to May) is also a beautiful season with cherry blossoms. But if you're interested in hot springs (onsen) in Beppu and Yufuin, a winter trip (December to February) could be magical as well.

Route and Accessibility:
All these cities are conveniently accessible by train, bus, or flights from Tokyo or Osaka. The Japanese bullet train (Shinkansen) can get you to Fukuoka, and from there, regular trains and buses can take you to Beppu, Yufuin, and Nagasaki.

Altitude and Acclimatization:
These areas are mostly at low altitudes, so there's no specific need for acclimatization.

Accommodation and Booking:
From luxury hotels to budget guesthouses and traditional ryokans, you'll find a broad range of accommodations. Booking in advance is recommended, especially during peak seasons.

Clothing and Essentials:
Pack according to the season:
light, comfortable clothing for the summer and warm clothing for winter. Comfortable shoes are a must as you will likely do a lot of walking.

Health and Safety:
Japan is known for its safety, but it's still a good idea to carry a first aid kit with essential medicines. Also, if you have any allergies, especially to seafood, always check what you are eating.

Local Etiquette and Respect:
The Japanese people are polite, and their culture is deeply rooted in respect and etiquette. When entering temples or shrines, follow the local customs. Keep quiet in public transportation and avoid eating while walking in public. It's also customary to bow when meeting people.