I am not sure if the following scentence is correct or if I need a comma (or a semi-colon) after "plays".
Joe enjoys plays but Emily prefers concerts.
any help would be greatly appreciated.
The following are correct:
Independent clause + Comma + Dependent clause:
 Joe enjoys plays, but Emily prefers concerts.
Independent clause + Semicolon + Independent clause:
 Joe enjoys plays; Emily prefers concerts.
Some writers feel the coordinating conjunction (e.g., but) is adequate separation in a sentence with short, balanced independent clauses.
Independent clause + Conjunction + Independent clause:
 Joe enjoys plays but Emily prefers concerts. <no comma>
If there is ever any doubt, use the comma, as it is always correct in this situation.