Location to do what in?

Nightlife, shopping (and if shopping what kind?), daytrips out of Tokyo, sightseeing (modern), sightseeing (traditional), sightseeing (neighbourhood hikes - unlikely in the summer), sightseeing (good connections to JR Yamanote and/or Metro to cover X Tokyo areas),proximity to pubs and izakaya, modestly priced speciality restaurants or upscale joints, etc, etc, etc...

Since you're going in July you probably won't want to deal with long walks to/from your hotel and anywhere of interest. That leaves out the Hilton, Westin and Sheraton Miyako (although when it comes to Location this Sheraton is absolutely the best placed hotel for my own needs). The Park Hyatt is also too much of a hike in hot weather and the shuttle to/from Shinjuku station was crowded and took forever the one time I took it.
I don't much like Roppongi but it is convenient for many visitors.
And the Mandarin Oriental isn't quite close enough to the Yamanote line for me to consider it ideal, but it is close enough to Tokyo and Kanda stations to be plausible and fulfills all the points I listed above.