September Plan

I am currently in the process of hashing out my itinerary for 9/5-9/12.

9/5 Arrive in Narita, for the hotel planning on something very close to a rail station in Tokyo for easy travel. Stay in Tokyo for the 5th through the 7th, definitely see some sights, do some shopping, and check out the arcades.

From the 8th till the 10th travel out to Nagoya.

Come back to Tokyo on the eleventh to finish sightseeing.

Go to Narita on the 12th.

From what I read the week pass would expire on the 11th if bough on the 5th, so I am not sure if it makes sense to get the JR pass for one round trip via NE-x from Narita to Tokyo and back, and also from Tokyo to Nagoya and back. Advice and what to do about the train passes would be great! Thanks.