Hi Hope,
I haven't really started digging down on my US short run custom printing research at this point, as my market is currently Oz. Mugs are goingt to be an interesting one for you I think. Most mug printers don't offer short run printing, they usually only offer bulk printing options. At least that has been my experience with the extremely limited amount of research I have done regarding items like mugs, gold balls and so on ...... essentially the gift/souvenir printing market.
The one that does stick out is Vistaprint, they do offer short run printing for both mugs and t-shirts as well, so they may well be a good one stop shop for you. Although I am only going by the Oz Vistaprint, I'm not sure what the structure is in the USA, I'm just assuming they would be offering the same services there as they are in Oz, but well worth checking out for you at least.
Good luck with it, hope you find a strong market for your creativity :)