Yep! For 19,000yen or under it's hard not to come up with a predictable recommendation.

However, The Strings IC for 19,000yen a night sounds like an excellent choice to me. Unless I could get Club floor rooms at the ANA IC, I wouldn't try for anything else. I can't imagine the rooms here getting any cheaper.


But as an acceptable alternative...
At the beginning of November, the Grand Prince New Takanawa (near Shinagawa station) is offering their Superior Floor rooms for 16,000yen + charges (around 19,000yen total) per night through Expedia.

It beats the standard rooms at the ANA IC hands down. Rooms were refurbished very recently. I'm not aware of any allergy issues except those that might creep through the windows from the magnificent gardens.
Be warned that the standard rooms here aren't nearly as nice and have not been rennovated remotely recently.

If you want to spend a little less, then I can also recommend the rooms at the Hotel next door - the Grand Prince Takanawa. At around 13,000yen per night for two people, I consider these to offer outstanding value. All the rooms here were rennovated about 4 years ago. Both hotels have non-smoking floors.

Please note that I do not hold nearly such a high opinion of the Shinagawa Prince Hotel.