IlliniGirl,
Not sure that you'll see my post before you get to Singapore. I was trying to find my Singapore food list, but I never did. The following is based on a trip to Singapore with my husband who lived there the first 22 years of his life.
Here's one of many websites on Singaporean food:
http://www.makantime.com
Here's what's at the forefront of my brain for Singapore (and I can't guarantee they are all spelled correctly):
Exotic fruits - mangosteen, durian (the famed fruit), and more
Lime juice - my beverage of choice
Pineapple tarts - different "grades/quality" at different places, a great gift to bring back
Lapis cake - this might just be available around Xmas & Chinese New Year, a multilayer Indonesian cake
Bah q tea - soup with pork served as a meal, two kinds - clear & brown broth, I like the brown one
Roti prata - basically a savory pancake that you dip in curry
Rojak - I refer to this as "Singaporean salad," a delightful combination of ingredients that are very tasty
Popiah - an appetizer sort of eggroll, but not fried
Chicken rice - sounds simple, but it's a huge thing there
Hot pot - I refer to this as "Asian fondue", but you cook the various items in a broth
Four Seasons - Sunday brunch, the best buffet brunch of my life
NY Dessert Café - sweets that are similar to what you're used to in the US
Indian food on a banana leaf in Little India
Takishamaya food court - Thai chicken wings
Takishamaya food court - Kaya; buttered bread spread with this coconut jam (kaya); I don't even like coconut, but this is great, especially good for hangover mornings; this is another good thing to bring home, it's sold in jars;
I'll post more as I remember. My lesson in traveling is "when in Rome, do as the Romans do." Singapore has a huge amount of good food available at great prices as long as you follow this rule and avoid the American places or any concept that seems out of place (i.e. Mexican). Try out some food that isn't available in Chicago. Many great meals are to be had at the "hawker stalls" throughout the city. Food courts are in the basement of many shopping malls. The food courts there are entirely different than ours here, so don't shy away from the great food to be had at the Singaporean ones. Most of the items suggested above are common and inexpensive.
As far as Hong Kong, I was there a short time, and we got a good spread free each morning at our hotel, but my one top-of-mind recommendation is that we had dim sum near a museum by the ferry. It was good dim sum and the view was nice. I can't remember the name, but I think this might be enough to help you get there.