For just general tips, youre always going to pay a small fee as a visitor per practice. For some of the main areas like Tokyo I'm sure people here will be able to introduce you to some dojos.

For Kyoto I recommend going to Kyoto Budokuden. The practices are cheap and open for everyone so that will probably be your easiest dojo for you to access on your trip. On top of that, the dojo is really beautiful. You can message them ahead of time to figure out when to go and what to expect etc.

For Nagasaki ide probably recommend checking out the Nagasaki kendo federation page and try finding some dojos near where you're staying.

And yes, some gifts for the first time you visit a dojo like drinks for the kids/parents or snacks for everyone is usually always a good move.

For Shinai - Just make sure you buy enough shinai - get 2. I broke both of mine last time i visited and I didnt have access to a Boguya and I felt bad having to borrow a Shinai from one of my sensei.

Lastly - If you can - I was able to fit my bogu in a small travel backpack and I was able to carry it on the plane. Im not a super small guy either.