Rather than Old Chinatown, I would recommend Clement Street, particularly if you're in a car. Clement Street is essentially the new Chinatown, with a bit of little Russia thrown in.
While you're there, there's Ocean Beach, and better chance of a sunny day on the west side at this time of year. Oh wait you said June.
may still be worth it, plus there's Louis' cafe, great view, and a real time machine. In any case it's on the way to the Golden Gate Bridge From Golden gate Park. As is the Presidio. Goldengate Park has the Academy of sciences, and the recently rebuilt deYoung Museum.
If you end up staying in a union square hotel Sears and Bluestem are great places to eat. The south of market area which tends to bridge downtown and Union Square to the south, has some great amenities, but overall is boring. Nevertheless the Museum of modern Art is there.
You might wish to consider staying in one of the two Japanese themed hotels in the Western Addition next to Japantown. Japan town is pretty interesting in another itself, and is also close to the Fillmore, which is also interesting.
On Fillmore Street itself you may not want to go south of Turk Street. Or for that matter, north of Broadway. Down the hill from Pacific Heights on Fillmore past Broadway is the Marina neighborhood, which is full of assholes. The Fillmore is also fairly close to the Haight Ashbury neighborhood, which is a shit hole.
If you must go to old Chinatown, end the day in North Beach. Sodini's, and Tony's Pizza, both Close to Washington Sq., Park, are great places.
Fisherman's wharf, including Pier 39, are complete shit holes. Stay away. Ghirardelli Square and the cannery are in this area, are hellholes and are full of flies. Additionally, San Francisco's skid Row are the blocks south of market Street between fourth and ninth streets.
The tenderloin isn't much better, however it can be fun if you're into slumming. If you are in San Francisco on a Sunday it might be a real hoot to go to a service at Glide church. Then you can follow all the codependent gay guys who went to church to Dotties true blue Café, which I believe is now on market Street.
Just west of the tenderloin, across Van Ness Avenue, near where City Hall is, is Hayes Valley, which has interesting boutiques And restaurants, including Moishe's Pippic, a good Jewish deli run by a very angry man. Also, Stacks is great for breakfast.
The mission has a lot of good restaurants, but in general is full of assholes.
As far as north of San Francisco goes, I've always found Gualala to be a good place to decompress.
Edited by Hayward - 4/25/13 at 8:24pm