Your Sunday looks a little scattered, running back and forth across town. Depending on where your hotel is located, I'd suggest starting in Shibuya and Harajuku in the morning. Spend what time you want there, then catch the Oedo subway line or the JR Yamanote + Sobu Chuo line across town to Ryogoku for the Edo-Tokyo Museum. Plan on at least a couple of hours there. Akihabara is 1 stop on the local train back into the central city so you could stop there on the way back if you have time. The flexibility is there if you are coming right back by there anyway.

I'd suggest changing your National Museum plans to the Japanese National Museum in Ueno Park. There are actually several museums there, although I like the main one near the back (north) of the Park. From Ueno, you could grab the Keisei Skyliner (or Express to save a few bucks) out to NRT and avoid going back into the city center to catch the Narita Express. I prefer the Skyliner anyway and the Keisei station is right outside the main entrance to Ueno Park.

If you have been reading this forum, you probably already know that July 25 will undoubtedly be VERY hot and muggy in Tokyo. Plan accordingly and try to avoid too much running around outside.