There can be little doubt that once you have arrived in the Chinatown-North Beach area, by far the best way to get around is on foot. Due to the busy and cluttered nature of both neighborhoods, and also because of the lack of parking options, driving around is certainly not recommended — especially in Chinatown. Buses can also be a help, particularly when you are going in a north-south direction or vice versa. Pedicabs (http://www.sfpedicabs.com/) also operate a route along the Embarcadero and through Chinatown and then North Beach. Stop one of them if they're empty and negotiate a price. For a bit extra many of them do walking tours of Chinatown.
There are many more parks, public seating, and cafes with curbside tables in North Beach, so why not see Chinatown first. That way, by the time you'd made it through its bustling streets you'll be ready for a coffee and a sit down in North Beach.