My watch has stopped after
The exact cost will vary depending on the shop you bring it to, and the overall condition of the watch. If the battery has just run out, it could be a very inexpensive fix ... but if the battery has died and corroded within the watch, it could be a much more difficult task, and cost a bunch more. If you are able to do so, I would recommend switching out the battery before you bring it anywhere as doing this yourself can save you some money and might get it running again in no time. As for replacing the face, I would recommend taking it to a repair shop for this (though once again I am not sure how much it would cost ... it depends on how much of the watch has to be taken apart to get the face off).
If your watch relies on a wound spring rather than a battery, then you would have to bring it to a professional to get the spring fixed (if that is why the watch has died). This is a delicate procedure, and requires a bit of skill and knowledge about watches to get it done right. This would be a bit more expensive to fix, but if your watch bears a lot of sentimental value, it could be worth it. If you have to wind the watch daily to keep it running, and winding it no longer works, then you are best to take it in to a repair shop and ask for an estimate.