While there is some diving in the north, the "better" diving is supposedly in the south, mostly around Kenting as well as Orchid Island. Orchid Island is logistically more difficult to get to and hence more expensive.
I only did a few shore dives around Kenting and was very disappointed. I can't recall the price, but it was expensive, viz. was poor, (maybe five metres?) max. depth was about 10 metres, there was little coral and the quantity of fish was very limited.
If you do go, bring your own equipment as the equipment for hire is of questionable quality. While I brought my own equipment, the guides didn't even have an octopus, but I suppose it may not be absolutely necessary with a max depth of 10 metres.
The guide on the first dive kept getting lost and had to surface a number of times to check out the landmarks on shore in order to get his bearings. Another dive was led by a local UW photographer who thought nothing of breaking coral in the way in order to get a shot. A miserable experience.
Unless you absolutely have to go, I'd give it a miss.
As Frogfish mentioned, the Philippines is close by, and there are also direct flights from Taipei to Palau, a reasonable 3.5 hours away.
Cheers.