For years my favorite style was the No Pouch Brief from Parr of Arizona.
http://www.nu-parr.com/product.php?p...cat=252&page=2
When I had worn out the two I had, I wasn't in Phoenix and couldn't find them on the Internet and have since settled on my new favorite, the 1.5 Classic Wonderjock from Aussiebum.
http://www.aussiebum.com/swimwear/760/black/
I think both of these would fit in the "bikini" category. Speedos are good too. I've never really gotten into wearing micros and thongs in public, though I've owned a few.