Hotels will handle it for you. If you staying else where, the owner is responsible.. But probably won't. It is a legal requirement to have filed.
If you just here on a 60 days TR visa and then leave.. Then you should not worry. Only when you do a 90 day report or extending your visa does a foreigner need to worry if tm30 was filed properly or not.
none of the discussions here is regarding 90 day reporting. It is the TM30.
Previously, it does appear the address for 90 day reporting and TM30 were the same. There is no official notice of change of mail address and both are active immagration offices, I assume they reroute mail as needed.
I can't really recommend a place... I did it the MOHW Taipei Hospital (in New taipei).. No appointment necessary, download the form from their website and bring them tk the ER. Do it in the morning, get results by 9pm if express service. Had to wait about an hour to get the test.