I recently did that very itinerary and had lunch at Lime Tree, which is relatively close... since the De Young is smack in the middle of GG Park you're in for a walk unless you take Melanie's suggestion and get dogs at Happy Belly.
Lime Tree was good, it's a bare-bones but cheerful little Singaporean place. We had roti paratha for appetizer, very nice, hot and flaky. I had Singapore noodles, which I wasn't crazy about -- they seem to err on the sweet side with their curry sauce. I noticed that all three of the kids at the next table had it, though. My dad loved his roast chicken, NOT something it would have occurred to me to order, but it had an appealingly crisp skin and I think a chile dipping sauce, plus rice on the side. I'd like to check out their weekend special of chile Dungeness crab.
King Won Ton, which Melanie reviewed recently for "bamboo" noodles and won tons, is also nearby.
Sorry, having trouble linking places!
Head over towards 9th & Irving (short walk from the DeYoung), and eat to your heart's content. In addition to the other fabulous suggestions already listed, there is Slider's (pretty good burgers), Gordo's Taqueria, Yumma's (fantastic Mediterranean wraps), Art's Cafe (wonderful divey coffee shop), Crepevine, La Fonda, Nan King Road (good Chinese w/some HK style items)... You get the idea. None of these places require reservations.
Surrounding the area of 9th and Irving is a plethora of restaurants.
Naan N' Curry is good for Indian standards at a good price.
Arizmendi has California style pizza slices which are excellent and cheap too.
There is also the new Persian place Lavash which I have greatly enjoyed the handful of times I have been.
Next door to Lavash is L'Avenida, which has pretty much been relegated to take out only, just two small tables jammed between the counter where people order and the wall.
There is a good Vietnamese place across from Lavash and L'Avenida on Irving St., but I can't remember the name.
I would skip Hahn's Habachi.
642 Irving St, San Francisco, CA 94122
511 Irving St, San Francisco, CA
1331 9th Avenue, San Francisco, CA
L'Avenida Mexican Grill
507 Irving St, San Francisco, CA 94122
I was there recently with my 9 yr. old daughter & ate at Park Chow based on CH & Yelp reviews. We were there for an early lunch so the place was fairly empty. I ordered the fusilli w/ shredded breast of chicken, sausage, & mushroom in a creamy tomato sauce and some hot tea (dd is into herbal teas these days). It was not bad but nothing to write home about either. Perhaps I should have tried the sandwich of the day or the Thai chicken salad but dd wanted pasta. Also, one order was plenty for both of us. After a while the table next to us was filled & the couple ordered some drinks. I heard the woman comment how delicious her watermelon mint drink was; don't know what companion ordered. Too bad I didn't pay attention to the drinks menu on the big board or I would have tried some.
DD wanted dessert but I convinced her she was too full to justify a whole order so I just got one scoop of pumpkin ice cream for her. It was very creamy but thought it was a tad sweet for my taste; nevertheless, it was hers & she finished it. The ice cream is meant to go with the ginger cake (a nice combo which I didn't order); so, I guess the sweetness would be offset by the cake.
I also noticed an Indian restaurant, Masala, a couple of doors away & a Mid Eastern cafe/fast food type of place nearby too. Never heard of these two before.
Enjoy the Chihuly exhibit, it is FABULOUS!