Glad you found this helpful!
Re: Uber Black - I requested it using the Uber app: it was pretty much the same experience as Uber anywhere else. Just select 'Uber Black Van' in the app. One thing that was different is the van had a taxi meter which was turned on for the ride, but everything was settled automatically by credit card through Uber like any other Uber. I also recall the final amount I was charged was ~1,000 yen lower than the original quote from the Uber app when I booked it.
As for Tokyo: we stayed 4 nights at a hotel next to Shimbashi station in Ginza. Definitely recommend the location as it was central to everything - and since Shimbashi station is on Yamanote line, it was also an easy direct ride to Shibuya / Harajuku / Shinjuku. Couple of other Tokyo highlights:
- Meiji Shrine (Harajuku): Definite must-see; an oasis of tranquility with beautiful architecture and great people watching (lots of locals in traditional Japanese attire, etc)
- Senso-ji Temple (Asakusa subway line): Another definite must-see; lots to do in the market streets leading up to the template (nibble on bites from the stalls lining the streets, souvenir shopping, etc). We also rented traditional Japanese attire and did a family photoshoot around the area - our kids loved the experience!
- Sanrio Puroland (Tama station - 45 minutes from Shinjuku): Spent a day here - kids are big Hello Kitty fans and had a blast! The theme park is pretty small but well executed and very 'experiential' with shows, photo opportunities with Sanrio characters, etc. It was also incredibly reasonable - just ~$80 for 2 adults + 2 kids with discount tickets bought online directly from the park - and a phenomenal value at that price.