What train goes directly from the Howard Beach Station to Central Park West?

The A train (of the A-C-E, the blue line). The A train runs between the Howard Beach Station and the 59th Street-Columbus Circle Station, which is at the southwest corner of the park (8th Avenue and 59th Street, aka Central Park West and Central Park South. The portion of 8th Avenue that borders the park is called Central Park West, and the portion of 59th Street that borders the park is called Central Park South. Also, the portion of 110th Street that borders the park is called Central Park North. However, the portion of Fifth Avenue that borders the park is NOT called Central Park East, for some reason).

Also, you can transfer at 59th Street-Columbus Circle to the Uptown C (of the A-C-E) or the Uptown B (of the B-D-F-M, the orange line). Both of these trains stop at several points along Central Park West: 59th and CPW (Columbus Circle), 72nd and CPW, 81st and CPW, 86th and CPW, 96th and CPW and 110th and CPW.

The A is an express train, so the next stop after 59th Street-Columbus Circle is 125th Street. Remember, 110th Street is the north border of the park. So if you want to get off at 72nd, 81st, 86th, 96th, 103rd or 110th, you must transfer at 59th to the Uptown C or B trains.