Full disclosure: This place is owned by the sister of a friend, and I was recognized when I went in today.
Classic Burger is an unassuming burger place on Hesperian in San Leandro. Their specialty is the classic burger, a hamburger patty topped with pastrami with monterey jack cheese melted over it and served on a bun with lettuce, tomato, onions, pickles, mayo, and mustard. This is the only place that I know of that adds pastrami to a burger but it's a surprisingly delicious combination. The fries are thick-cut, crunchy on the outside, creamy and hot on the inside. The onion rings are also pretty good. The milkshakes were rich and creamy without being too sweet. Everything is cooked to order.
The owners run the place and are among the friendliest people you could ever meet. Their kids are usually there doing homework or playing and it feels like you're eating in their home. Maybe I'm biased but I would love to see them succeed. :)