In reverse order of excellence in the Pattaya area:

‘Nang Nuen’ on ‘Walking Street’ is good and, if you are just passing through Pattaya something of a show.

Mum Aroy in Narklua, excellent sea food, but getting rather pricey.

In Jomtien, ร้านอาหารสุดทางรักพัทยา, this is not a place with live fish to gawk at and choose, but the seafood is sublime.

To the south of Pattaya towards Satthahip Phreecha, I’ll not argue with anyone who claims this to be the best seafood restaurant they’ve ever eaten at. (and yes live fish, prawns, cabs etc).

To the North of Pattaya near Chonburi at Saen Suk, Wang Muk sea food restaurant – There is no better sea food in Thailand and the reason why I would not argue with anyone saying Phreecha is the best is because I’d know they’ve never been to Wang Muk.

Sea food markets of note:

Narklua market (at the back of the old market nearest the sea)
Wang Muk sea food market
Ang Sila sea food market – really really superb.

For the past 9 years I have lived in SEA port cities and Bigal1’s advice is the best. Go to the fish market at the harbor and buy the best fish, have it cooked for you in a small place nearby and be happy.
In Thailand really good seafood costs as much as in the west. Check for Seafood Market in Bangkok. Good place but not cheap at all. The places mentioned by persona are ok but nothing mind blowing, standard fare serving the Thai middle class.
Yes, people do fish in Thailand but the catch is limited and mostly reserved for export or privileged consumption. The tons of shrimps, baby lobsters, crabs, snappers etc. you find all around have never seen the sea. The romantic belief that fishermen go out in the early morning, bring in a colorful fish and you have it for lunch and at a bargain is tourist industry image. Resellers wait with their cellphones in the harbors, check the catch, and get immediately limits from their patrons in the capitol or Japan. If the harbor is close to an airport, the good quality is within hours in Tokyo. Only rejects enter local wholesale or those ordered by places like the restaurant above which charges a premium.
Islands order wholesale frozen farmed fish. I have seen it on Koh Samet and do not think other places are any different – this applies also for fish restaurants in Pattaya. Difference here is that the farmed fish is delivered alive to the better places – but again this is not a catch from the sea.
I do not eat fish away from places like Bigal1 described. The danger of formaldehyde (causes cancer) and other forms of manipulation is just too big. Shrimps are another long story. Just take a look at the farms north of Ayuthaya (that’s not on the sea).
In sum, if you are not at a good place and islands are not, if you do not go at the right time, and if you are not willing to pay a realistic price for the product you wont get good quality. In my place it is either at dawn or dusk and it is rubbing shoulders with locals and being prepared to pay a dollar more than them.