Trip to Osaka
 

I have to go to Osaka in March, and then to Hong Kong (haven't been to either place).

Since this will be my first visit to Japan, I was trying to figure out what I should do if I want to spend a couple of days in Japan. I don't want a very busy itinerary, since I like to linger and enjoy a particular area, vs checking boxes.

I was either thinking of combining Osaka with Tokyo, or with Kyoto, or just doing Osaka. I will be flying in from Denver (*A flights) and thought about either flying into Osaka, or taking the train from Tokyo. After Osaka, I have to get to Hong Kong, so I don't know if that should play a role for my itinerary.

Just to be clear, you will have two full days in Japan? And you're arriving in and departing from Osaka? If so, I recommend getting a hotel in Osaka, then go to Kyoto for a full day (30 minute train rain from JR Osaka station) and spend a day wandering around Osaka. You'll have no time for Tokyo. Here are some websites to give you ideas.
https://www.japan-guide.com/e/e2157.html
https://www.japan-guide.com/e/e3950.html

I can spend as many days as I want, in Osaka, I just have to be there for a particular meeting. So I could split it up with x days here, and x days there. Then I have to go to Hong Kong.

Recommendations will depend totally on how many days you'll have in Jpn. Your meeting is in Osaka? If you're spending anywhere from 2-5 days in Jpn, just stick to the Osaka area. From there, you can make day trips to Kyoto, Nara, Kobe and/or Himeji.

There's plenty to see in the Kansai (Osaka-Kyoto-Kobe) region. I would recommend Kyoto and Nara, the two ancient capitals, and Himeji, just a short Shinkansen ride from Osaka, to see the wonderful original samurai castle. (The one in Osaka is a concrete reconstruction.) Save Tokyo for another trip.

If you can fly in and out of KIX (which North American airline people tend to refer to as "Osaka," although it's way out of town) that will probably be the most convenient arrangement. It doesn't have a lot of flights from North America, but it has a lot of flights to other parts of Asia, including Hong Kong.

If you don't know what to see, I suggest buying or downloading a guidebook to Kyoto. Since all the major cities in Kansai are pretty close together, guidebooks for Kyoto also contain information on Osaka, Kobe, and Nara.

Since you fly *A, KIX is easily reachable via SFO on both UA and NH and that has been my route of choice from California. From DEN, there are many options but most require a change at NRT or HND or the aforementioned SFO.
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Thanks for the advice. I am flying into and out of KIX and will be staying in Osaka for the duration of the stay. I'll make excursions to Kyoto and other cities as recommended.

You mentioned earlier that you like to ramble at a leisurely pace. The general Namba area of Osaka is good for that. Lots to see from say Shinsaibashi walking towards Dontonbori/Namba area, then on to Den Den town and over to Tsutentaku. You could walk it all at relaxed pace for a day. Just an idea.