With the budget, I have to agree it’s hard to find a true luxury hotel in these cities.
Besides W in Taipei, you can also look into Humble House (member of Design Hotel). Just a stone throw away from W, location is ideal, the rooms are well-designed and well-priced. We used to stay at the W, but the neon lights, loud music and “see and be seen” scene just became too much for us after a while.
For HK, I highly recommend MO Landmark. However, there’s lots of great boutique hotels worth considering if you don’t care for a full-service hotel with a huge pool, gym and multiple restaurants - Pottiger (great Central location, spacious room), Lanson Place (SLH property, in Causeway Bay), Upper House (well designed room, in Admiralty).