Love staying at the Conrad during holidays. I actually live in Tokyo, but when I have extra expiring FN certs I can't use, I end up burning 'em on Conrad Tokyo!
For people coming on a personal budget with a family, the most budget conscious is:
1) Keisei Main Line Express for Haneda Airport (direct train, 1 hour, 14 minute, 1,280 yes) -> this train goes straight to Shimbashi but seats aren't reserved.
1a) If there no upcoming train in a reasonable time bound for Haneda Airport, then take the non-express for Ueno and switch at Keisei Narita. Cost will be the same.
Enjoy!