Yes you can fish off the beach in Pattaya. I see Thais fish off even Pattaya Beach.
Sometimes I see people fishing off shore by the lighthouse. Passed the pier and Walking street.
You will also find people fish in Jomtien and Naklua. I have never seen a foreigner fish there. Most foreigners who fish, that I know of, like to fish off the boat but that may be too spendy for some.