We have just completed a 5 night stay at Midori's fantastic apartment in Shinjuku and we had a wonderful time. The apartment was exactly what we were after, was very nicely decorated and very comfortable. It's nice and modern and we found it had plenty of room for our family of 4.
It had all we needed to make ourselves feel at home for those 5 days and was in a great location. You're close to some busy train lines but honestly, we never even noticed them going past. Being so close to the lines made using the train system really easy (it's only about a 5 minute walk to a station) and this made it super convenient. There are several good supermarkets/convenience stores nearby which made buying supplies nice and easy. Quite a few decent little places to eat around the neighbourhood too which was awesome. You're close enough to walk to the main area of Shinjuku which we did numerous times and only a 'stone's throw' from some great sites.
Midori was a fantastic host and very easy to communicate with. Check in was very easy and the instructions/navigation map/check in materials she sends made finding the apartment very easy too. If we come back to Tokyo, we'd definitely be in touch with her to stay again!