I used to live in Tokyo and even stayed in one of your choices.
Dai-ichi Hotel is near Shimbashi (or Shinbashi) Station (Japan Railway and Metro subway) (Central Tokyo)and within walking distance to Ginza. It's the oldest hotel of your 3 choices but close to "local" eateries under the railway tracks and side streets. Also close to a few of the fancier restaurants in Ginza and Shinbashi. More of a "businessman" hotel, maybe not so cosmopolitan as the other two.
Prince Park Tower is a new hotel completed around 2004/5 and is literally in a park (Shiba Koen or Shiba Park) next to Tokyo Tower (the orange painted Eiffel Tower lookalike). The nearest subway station is Akabanebashi (Oedo Line that connects with Roppongi and Aoyama and Shinjuku (new business district). It has both Japanese and Western clients (business and tourists) and restaurants. The famous Zojo-ji temple is nearby where you can see trees planted by famous people like US President Ulysses S Grant. The old main Prince Park Hotel buildings are in the old temple grounds. This new hotel tower annexe is a few hundred metres away. There are no other buildings within 200m of this hotel tower so finding it is easy except that the subway station is inconveniently far. The naughty Roppongi district is walking distance up the hill from this hotel. On the other hand, the pronunciation in English is almost like what the Japanese would say: "Shi-ba Ko-en No Ho-tay-ru Pu-rince-su Par-ku Taa-wa" for the taxi driver.
Park Hotel Shiodome is the funky new designer hotel in the Shiodome Media Tower across the street from Conrad Tokyo and Gordon Ramsey's eateries. Shiodome is the latest Hot Spot on Tokyo Bay overlooking the Rainbow Bridge. Again, minutes walk from both Ginza and Shinbashi. Nearest subwy station is Shiodome Station on the Oedo Line....although another similar named station is actually suspended in the air as this section also has a monorail (Yurikamome Line) that leads to the entertainment playgrounds of Odaiba island across the Rainbow Bridge. Also walking distance from Shimbashi station if not carrying anything. I'm biased as my apartment was in Shiodome, so I would choose this hotel as it is close to lots of tower blocks with hundreds of restaurants and bars.
Happy trails,
MTF
