If you are using the 250 dollar voucher, I would use the New Otani in Osaki. Although it is not as "nice" as the Hilton. It is nonetheless acceptable. Also, to see the sights you stated. The location of the New Otani is perhaps a little bit better. Additionally, you will get more for THEIR money, in terms of number of nights in the hotel.

One last thing, the only drawback I would see with the New Otani is getting there from NRT. You will have to take the Narita express to Shinagawa then transfer to the Yamanote line to Osaki (1 stop I believe). With the Hilton, you can take a limo bus all the way to the hotel.