There are many qualified watchmakers in & around the NYC area that can handle the task of overhauling/servicing a rep watch. If the rep is powered by a Swiss-made ETA movement, then pretty much any watchmaker can get parts (if needed). However, if the movement is a low-end Asian-made movement, parts will be problematic. Check with the rep seller to see what brand & model of movement is in your watch & then let your fingers do the walking through your local telephone book (watch & clock repair or similar). Phone the watchmaker & ask if they work on ETA-powered replica watches. Some watchmakers will & some will not. Calling 1st will save you alot of wasted time.
An overhaul on a standard 3-hand rep watch should run $100-$200 (NYC/Westchester areas are likely to be at the high end of the scale). If you have a chronograph, expect to pay considerably more (plus parts, if required).