I don't care for the market near the Ace Maestro store - it's in one of the worst parts of Surquillo and the odor is awful (just my opinion - my mother in law does a lot of shopping there, so what do I know!).
Surquillo has two very nice markets.
Mercado 1 is one of Gaston Acurio's favorite places. It is at the puente on Ricardo Palma, just to the north, in a big building that says "MERCADO" - the block around it is mostly pedestrian traffic and there are lots of nice little restaurants tucked in there.
Mercado 2 is on Calle Dante, just a block off the via express where it crosses with Angamos Este. This is my favorite market for shopping for meat, and in general it's usually a tiny bit cheaper than #1.
There are maps to both of them on the post here - http://mylifeinperu.com/2010/05/07/surquillo-market-1/