Get on to a handler in Tokyo ASAP so you can sort out your landing and departure slots. I haven't been there for a few years, but it used to be that you were assigned an airport depending on slot and parking availability. Both airports have their pros and cons: notably, Haneda is very close to downtown, whereas Narita is a long way out of town.
We sometimes found that our preferred slots were simply unavailable, and had to adjust our schedule accordingly. Hence the advice to get your handler on board as early as possible. We used to use Noevir - not sure if they are still around. I heard that a few handlers went under after the tsunami and nuke leak.
Taipei (Taoyuan) RCTP has had a dedicated FBO for some years now, and you are well advised to use a handler who has access. Parking away from the FBO will probably require you to walk back and forth through the commercial airline terminals, which can take some time. If your pax have contacts at high level in Taiwan, you might be able to land downtown at Songshan RCSS... check with the handler, you can only ask!
Last time I went to Phuket, the local authorities bounced us due to parking restrictions. We ended up in Bangkok, which at the moment might be a less desirable destination than it usually is. Make sure you sort out overnight parking in Phuket, if required.
There is only one handler worth using in Bali... Dude (pronounced 'doo-day')! He and his team will take good care of you, and don't be shy about accepting his hospitality, if offered.
Safe flying