There are very few places around downtown to have a drink and cigar, but this is one of them. Stocked by Churchill's cigars; a local cigar shop, Rum Bar has a reasonable selection of about eight or ten cigars and a bar full of rum and a mixologist to go with it. If you're into rum drinks this is also one of the best spots in town to get one.
There are definitely a handful of shops in the area you can pick up a cigar, but none of them are open past 8 or 9 pm, and none of them will serve you a cocktail while you smoke. When I'm out with the pals and in the mood for a cigar, it's generally not before 8 pm. You've got to have a bit of forethought for that, and I'm rarely blamed for foreword thinking, that's for sure. Sure the drinks are premium priced, and the cigars too, but this is the spot when you're looking to pair them up.
Note that smoking is only on their outdoor patio, and not in an inside lounge. It would be nice to find a spot with an inside smoking lounge in the downtown area, but beggars can't be choosers, right? :-/
Happy Yelping Phoenix, see you around downtown!