The answer to your question is... it depends.

Here's my vote for the Conrad:

I like the transport connections at the Conrad. It offers somewhat better access to Narita Airport than the West side of town. Narita Express to Tokyo Station and then a taxi is quite a nice way to arrive. (Trains all the way to Shimbashi is also very do-able).

From the Conrad, you have the Oedo line right on your doorstep - which means good access to anywhere on that circular line around Tokyo. You are also in walking distance of Shimbashi for various subways and JR lines. FWIW, you are also within a stone's throw of the Yurikamome line...

True - It is a "bit of a walk" to Shimbashi station, but I find it to be quite a pleasant one if you use the elevated pedestrian "boardwalk." (Not so pleasant in a howling gale - but ...).

The immediate environs of the Conrad are rather "sterile" at night, but you can walk to Ginza from there - and that's a very lively neighbourhood in the evenings.

If your plans are to take Shinkansens from Tokyo station (or Shinagawa station) then this is a better starting point than the Hilton.

(If your plans are to see Mt. Fuji then Shinjuku wins...)

But really, the answer to your question is.... it depends.