I've had a couple of check-ups over the last year (complications with kidney stones make some of the symptoms of STDs a little similar).
I tried the govt clinics but I've always found the appointment and waiting times to be a little long.
Depending on how you're feeling and what your budget is, MenHealth provide a nice service - 2 locations, one in TST and the other in Central.
I always hits TST for fear of bumping into someone I know.
The only downside is the STD Dr is separated from the others on premises, so it can be a little obvious what you're there for.
They email the results to you if you prefer and I've found them to be helpful, non-judgemental and quick.
YMMV
http://www.mhs.hk/web/en/index.php