From what I've seen.
The Westin has:
bigger rooms
better breakfast buffet
more things to do nearby

Prince Sakura has:
closer train station
nicer looking rooms
whirlpool available

Which do you recommend?

I have 2 weeks in July. I'll be getting a Green JR Rail Pass. Most likely flying to NRT.

I plan on:
Nagano (trying Hokuriko Shinkansen Gran Glass a least 1 way) - 1 day
Hakone (near Mt Fuji)- 1 day
Osaka (2 days starting Tue, Wed, Tokaido Shinkansen, stay at the Singulari) - USJ, Dontombori 1 day - Osaka Castle, Abeno Harukas, Umeda Sky Building, stop in Kyoto, on shinkansen by 8:30 back 1 day
Odaiba & Maricar at Tokyo BBQ - 1 day, will have internat'l driver's license
Akihabara/Asakusa - 1 day, night Yamatabune dinner cruise
Disneyland - 1 day, Tues or Wed
DisneySea - 1 day, Tues or Wed
Shinjuku - 1 day including Robot Carnival, 1 hour in love hotel
Enoshima, Kamakura, or Zushi Beach - 1 day
Yokohama - 1 day, Shin Yokohama Ramen Museum, Chinatown, Cosmoworld, CupNoodles Museum, Landmark Tower at night

11 out of 14 nights. Will include Shibuya and other stuff. My wife will wear clothing that covers her arm tattoos.

Any advice is appreciated.