Don't do it on a weekend. Many places still only work half day on saturday and closed sunday.
Obviously folks that work all week shop on the weekend too so the stores that are open are packed.
Save U supermarket carries a good stock and is often considerably less in price than here on the island.
The one big thing I notice is a pack of 26 huggies diapers here costs around $49 and I have bought at Brodies and Save U the exact same package for $37.