At Chinatown, stop by and buy some bakkwa at LimCheeGuan. They have prawn and fish bawkwa which isn't common and I like it, and the signature pork bakkwa is very good especially if it's hot.
Bakkwa (pork/beef jerky) generally cannot be brought back to USA, chicken/fish I haven't tried
Lim Chee Guan New Bridge Road Store+65 6933 7230.
https://maps.app.goo.gl/19x617iXsDU3apPKA
As for food: ou could find places where there's a mix of stuff.
Eg for Chinatown Point (daiso), it's a mall with restaurants ...
Next to it is Hong Lim complex (hawker center). Take a walk around the hawker center, anything interesting to eat. If you don't like it, then go to one of the restaurants in the mall
looks like this:
https://youtu.be/L9bzCMWDiWI?si=NIVYzrYSWYppPIcU&t=881
If you don't like the outdoor heat/humidity, some malls have indoor food courts that would be similar (but not as much variety and taste won't be a good ). I don't believe there is one at Chinatown Point, but Tiong Bahru mall has one
Kopitiam @ Tiong Bahru Plaza+65 6276 2325.
https://maps.app.goo.gl/7VFmPCDGnUp4qsjg8
buy a meal each (4-8 sgd), get a kopi/teh(1-2sgd) or bubble tea (3-5sgd), split a dessert (2-4sgd - tofu pudding with multiple toppings, ice kachang/shaved ice)
Whatever local cuisine, it's likely to find sauces at supermarket (NTUC, cold storage, Sheg) that you can bring back. Prima Taste and Seah's are pretty good taste-wise. You can actually find the more common Prima taste products at your local USA Asian supermarkets (laksa noodle/sauce).
https://www.primataste.com/our-products
https://www.seahsspices.com/products
Dry spices, I've brought back, declared it, gone thru usa secondary customs where they looked at it, multiple times without issues. The complete meals - if it has meat, may be a problem.
And of course kaya spreads. You can get kaya toast (for breakfast, or anytime during the day) at hawker center, food courts, standalone cafes like Ya Kun or breadtalk/toastbox
https://www.fairprice.com.sg/category/kaya