I've always liked the offerings at Hank's Oyster Bar.
I have also enjoyed the oysters at Legal's Seafood in Gallery Place/Chinatown. I know its a chain but its high quality. Many times when I am going to see a movie I will grab a Sam Adams, some oysters, and a cesar salad at the Legal's bar before or after the show. It thrills my Boston heart :)
I had to dig for a while, but here's what I found on the Clydes website. Half off is an amazing deal - try one of the Orca platters with a friend or group. They have never listed prices on their website.
OYSTER HAPPY HOUR
Join us for Oyster Happy Hour, during which all raw bar items are half off.
Clyde's at Mark Center
Monday through Friday, 4:00 -- 7:00 PM and 10:00 PM to midnight.
Old Ebbitt Grill
Monday through Thursday, 3:00 -- 6:00 PM and 11:00 PM to 1:00 AM.
Clyde's of Gallery Place
Sunday through Thursday, 3:00 -- 6:00 PM and 11:00 PM to 1:00 AM.
Tower Oaks Lodge
Monday through Thursday, 4:00 PM -- 7:00 PM and 10:30 PM -- 12:30 AM.
The Orca platter at the Ebbitt is maybe the best deal in town:
-One 1 1/2 pound chilled lobster
-12 crab claws
-12 oysters (raw)
-12 claws (raw)
-12 shrimp (gigantic - size of your palm)
During the happy hour, I believe this entire plate costs around $45. Even without the orca platter, Ebbitt is the best place in town for Oysters. Good selection, always very fresh, and the half off happy hour is one of the best deals in town. I would gravitate to the back bar if you are looking to avoid a lot of tourist traffic.