3 weeks in Japan in June

While I can't help you with the name of a travel agent--there are others who can--I just wanted to mention that it's very hot in Japan in June. Well into the high 80's and low 90's (F) It's also a very rainy month. Be prepared.

If you are looking for a group tour, we love Gate 1 Travel.
https://www.gate1travel.com/asia-pacific/china-japan

If you don't want a full group tour, just day tours, use the internet for local tours or TripAdvisor.com

Do not miss Kyoto.

Inside Japan did a great job for my trip in November.

https://www.insidejapantours.com/us/

I took one of their organized tours (Classic Japan) but also used them to make arrangements for independent travel after my tour.

One of the forum members (vandrabrud) used Inside Japan to arrange a trip and wrote a trip report about her experience. I found the report extremely helpful and that is what led me to Inside Japan. I’m linking her report below:
https://community.ricksteves.com/travel-forum/beyond-europe/first-trip-to-japan-trip-report

Weather-wise, I’d rather be in Japan in June than in July and August. Later in the summer is hotter and more humid.

We did Japan in September and it was perfect.

I've been several times and have always planned my own trips; it's very easy and this is a helpful website to get your started:

https://www.japan.travel/en/

You should also know about the GoodWillGuides, an association that provides you with a volunteer guide at the destinations of your choice. You are expected to pay only for shared transportation and meals.

We did this in Kyoto a few years ago.

https://www.japan.travel/en/plan/list-of-volunteer-guides/

The main sites of tourist interest are quite easy too get around on your own, despite the language barrier, and we found locals so kind and eager to help.

One experience I recommend is to spend a night to two in an onsen hotel where you can relax in the Japanese hot baths, sleep on tatami mats and dine on local food. This is the one we chose and it was quite an experience!! We had our own private bath, rather than a shared bath that is more usual. Look at the RYOKAN COLLECTION website for information on all of these traditional Japanese inns.

https://www.ryokancollection.com/ryokan/kayotei/

Never used tour guide we have always just planned our own, which is easy enough to do.
With the train system its very easy country to tour effectively. We were there last year for the third time and it seemed really cheap in comparison to lots of places in the world. (not something i ever expected to think)
One thing i would really recommend is going to a ball game as they really are unique - the enthuasm is amazing and they are pretty cheap and most are easy to book in english. Never been in June before but have been in May and must confess a place i would go anytime when i get the chance.

Another vote for Inside Japan. We did a variation of their Traditional Japan self guided tour last year, and it was excellent. They book hotels and ryokans for you according to your preferences, as well as train and bus tickets, and any guided day tours and activities you would like. It’s very customisable. They also provide suggestions for what to do in each location. We found it all very easy to follow, and everything went seamlessly.

We also used InsideJapan this past March. They helped us plan a 3 week trip for 4 adults.
Also, I left my iPad on the plane going to Tokyo. I emailed them the next morning and after some verification emails, (description and my seat number) they had it delivered to my hotel 1 day later. All I had to pay was the delivery charge which was under $10. Great service.

Happy New Year everyone! Thank you so much for taking the time to help and share your knowledge. This trip is a  high school graduation present to our son. As with so many teens, he has always wanted to see Japan. In addition to seeing the famous sites, experience the culture, cities, people and food we are also interested in experiencing nature that’s unique to Japan. We are based in the US and have been to most of its NPs. According to my research June is a great time to visit Hokkaido. As first time visitor, I’m wondering if we should spend a week in Hokkaido and the rest in Honshu. Or all 3 weeks in Honshu and experience nature there without the extra travel. We don’t want to be on the go ALL the time so I have reservations. After Japan we are also spending 3 weeks in China. Please advise. 

You definitely should spend some time in Hokkaido. The Shiretoko National Park (walk around Shiretoko 5 lakes) and the Kushiro marshlands with the protected red-capped cranes are striking areas of nature. The various historical museums (Abashiri prison, 7th army museum, open air Hokkaido village outside of Sapporo) are also interesting. The flight from Tokyo is short if you are not spending time in Tohoku. Does your son read manga? The Golden Kamuy series might interest him.