Near City of Hope?
Duarte's a bit of a dining desert, and City of Hope being wedged in between a residential neighborhood, Santa Fe Dam, and the 605 doesn't really help matters much. If you're willing to drive a few minutes there are more and better options to the west in Monrovia and to the east in Azusa (search various threads here for more on these cities).
If you need something closer, and don't mind cheap and no atmosphere, El Salvadoreno on Buena Vista and Huntington has some first-rate Central American comfort food. Green Burrito is also OK, as is the Filipino place near Highland and Huntington (name escapes me, but good chicken). Otherwise there's not much in Duarte, unless you can stomach the Spaghetti Factory, which I usually can't...
La Paloma, just down the street from City of Hope on the corner of Duarte Rd. and Buena Vista Ave. is above average Mexican food and Tommy's (not the Original Tommy's) right behind it on the Buena Vista side is a decent hamburger stand.
Villa Italia in the Target shopping center on the other side of the 210 is a pretty good Italian restaurant and the new Bourbon St. Bistros (yes, plural and abbreviated) has good Creole food, on Huntington between Highland and Mt. Olive.
J&A Cafe in the Mike's Food shopping center (corner of Buena Vista and Huntington, behind Carl's Jr.) is really good for breakfast.
I believe the Filipino place Bradbury is talking about is called the Green Banana Leaf and it's in the back of the complex, not real easy to see from the street - kind of across the street from 7/11 - which reminds me that Le Donut next door to 7/11 has some really delicious donuts.
No, there's a dirt-plain Filipino place right on Huntington, on the south side of the street a bit east of that shopping complex. Very cheap and very cheerful - we were in there one day and it seemed to be run (at least for the afternoon) by a bunch of kids. Quite delicious stuff, and no I can't recall the name.
Here are some:
Joe's Place: on the corner of Buena Vista and Huntington (in the Big Lots mini-mall). They serve some pretty good sandwiches.
Janet's Mediterranean: on the south side of Huntington (across from Joe's Sandwiches)
Peach Cafe: downtown Monrovia. Good atmosphere. Good food.
La Paloma: corner of Buena Vista and Duarte. Their gorditas are very good.
Canyon City BBQ: located in Azusa, which is just a few minutes drive away. Their brisket is really good.
Basil Thai: in Arcadia on Huntington.
Chang's Thai Bistro: in downtown Monrovia on Myrtle.
Avoid Young's Gourmet.
I used to take my mom to City of Hope pretty regularly. We almost always had lunch at Din Tai Fung - which isn't very far away at all. (I am one of those who think there are a lot better XLB to be had in town than at DTF, but for lunch near City of Hope, it always seemed like a good choice.)
Yes - if you want to go back west into Arcadia, DTF is a right turn off Duarte onto Baldwin. A favorite lunch spot of ours is Chang's Garden, which I believe is Shanghainese, but it's very good no matter what you call it. It's just at the eastern entrance to the last shopping mall before Baldwin. Not only good food, but also about the friendliest Chinese place we've ever been to.
There is also Thai City which is a good Thai restaurant. From City of Hope go east on Duarte Road which will turn north and become Buena Vista. Continue to Huntington Dr. (2nd light) and turn right. About 1/2 mi on the right.
Caters to American palate so not too spicy. But they can always amp it up if you ask.