Maybe the market you’re referencing is Polvos Azules. It’s kind of a cheap shopping mall with lots and lots of different little stalls selling everything from clothes to sneakers to electronis to artwork. Across the street from the Sheraton.
In Miraflores, there’s a great Peruvian restaurant worth going to called La Mar. It’s only open for lunch- try to get there early since there’s usually a wait. Great ceviche.