I have an old Specialized Hardrock mountain bike frame in great condition that I am restoring and using to build a bike from scratch. I want this bike to look very good, everything is either new or being repainted, and all parts will more or less match.

I don't like exposed brake/shifter cable. I think it looks bad and (especially when building the bike myself) is just another place to screw up the housing. I was thinking of running the cable next to the existing cable stops, but wouldn't that look like dirt? I know I can take a dremel tool to my cable stops, I just can't decide if it's worth it or not.

Exposed cable is functionally superior. When you run cable housing the whole way, you get the compression of the housing for the entire cable length which creates an excess of lost motion. When you take it to the cable stops, you're essentially getting the stiffness of the frame material instead, which is much less compressible than cable housing, so there is a lot less lost travel.

in my opinion removing frame bits doesn't really go along with the word "restoring." My opinions of what looks good on a bicycle were formed in an era where only cheap bikes had brake cable stops, but all the frames I've made recently have them because that's been the style for quite some time.

+1 on the 2 above, use them as is.

Brian