Chinatown is just northeast of downtown LA on Broadway. Its about 10 blocks long but the center of activity is Central Plaza.
This place is adjacent to Olvera Street (the originating block of land for the city of Los Angeles) so you should DEFINITELY do them both in the same day.
Chinatown is a great place to visit. It has a multitude of shops and restaurants with their own personalities. You can buy some of the good are jaw-dropping prices!