As an alternative to the Millbrae dim sum places, I recommend Hung To Seafood in South San Francisco. My boyfriend introduced me to this place and I thank him every day! For the price, the dim sum is great. Dishes range from $2.40 to $5.00 a plate. Some of the best har gow and sticky rice in lotus leaf that I've ever had. Very fresh, especially the seafood, and the portions are nice for the price.
Unfortunately, you will likely need to take a cab there (I don't know of a convenient way to get there via public transportation). But it would just be a short ride away.
Address is 221 South Spruce Ave., South SF
Phone: 650-877-0828
I think they serve dim sum until 3:00 pm.