What size tires are those? 26x1-3/8"? As others have stated, it's hard to nail down make and model as so many of these entry-level bikes were OEM-ed for numerous outlets under different brands. The pump pegs on your frame would indicate an older, slightly better model frame than those Falcon components would imply. Since you bought the bike from a shop with new tires, etc. they could have built up the frame with said parts too.
It looks like an old high tensile steel touring frame, probably why it feels so smooth. Either way, it's the perfect bike for running around NYC, crossing the Williamsburg, riding to Greenpoint and hitting up the cafes and restaurants on the weekend. (born and raised in NY...know the city well.)

My wife's girl 10-speed is built very similar to your's, with the exception that your frame is nicer. The brand of her bike is Galaxy II. I suspect it's just a generic unknown brand.