Simply Japan. We went for three weeks in 2018, on a self-guided tour with them, and I cannot recommend them too highly.
Your itinerary sounds like exactly the kind of thing that they would recommend for two weeks, and can be easily done on the bullet trains, which are as amazing as everyone says.
I would use them because Japan is very strange and confusing, but this cuts two ways. One it meant that they could recommend good places to stay, and sort out the bookings, and all of the difficult stuff was easy, but they could also get us into some of the less obvious places. We spent three nights in onsens, the traditional inns with hot water springs. We'd never have done that without them, but these were some of the highlights of our visit.
For me the trip was a perfect balance between organised and not. We weren't part of a tour, but had a huge document which told us exactly what to do, and with cars and train tickets arranged (and believe me, you need instructions to get out of a main Toyko station with 34 exits). We had guides for a half day on some days, on other days we did our own thing. We did have a guide who took us around the manga area, and they also got us tickets for the Ghibli museum, which are really hard to get hold of.
I cannot recommend Japan, and them, too much. It was supposed to be a once in a lifetime trip, funded by an inheritance. We are going back next year...