I do smoke some cigars with bourbon or rye, but it depends on the cigar as flavors of both can be destroyed if not careful. Bourbon/rye/cigar combos can be flat amazing though.
Apparently, drinking bourbon at 6AM is frowned upon in this establishment

, so coffee seems to be an acceptable choice.
Maybe I am a lightweight, but if I am smoking a really strong cigar, I usually grab something with carbs in it to have sugar in my system.