What do you use to clean off tar/asphalt from the outside of the tailpipe?

 

if its metal, neverdull by eagle one

 

I have to assume that you are talking about the chrome beauty tips, I have had good luck using a citus based bug and tar remover called 1lifter or Lifter1 (the way the logo is designed, its hard to tell which way to call it.) It can be picked up most auto parts stores. Remove the beauty tip (if possible), spray it on, let it sit for a few minutes, wipe off. For heavier amounts of tar, several applications may be needed. Then polish using Neverdull or any other metal polish (Brasso, Tarnix...)

Another hint, when replacing the tips, coat the bolts with Anti-Sieze, it will make removing them the next time for cleaning 100% easier!!!

 

Would metal polish also help remove a caked on black stain on the inner side of the exhaust tip? I've tried using #0000 steel wool and it still wouldn't come out.

 

I guess that it would depend on what the stain is... if it is just like carbon from the exhust gases, with enough work, yes, it should come off. I personally try to make it a habit to take the tips off at least once or twice a year to give them a complete cleaning. I could probably do it more often, but then that would be over kill, IMHO. You might also try using a bug and tar remover to clean up those carbon deposits, not sure but that may help. Another alternative might be to try and use something like 4* tire and rim cleaner, it does a hell of a good job loosening break dust, it may just break up those carbon deposits too.