If i am doing an am cigar which is not often, I drink coffee or expresso. Really enjoyed this when I went to Italy a couple years ago. i only do it when I am on vacation or once in a great while on a sunny Sunday when I got lot's of time to relax.
I like to have a beer or wine when i smoke in the evenings sitting out back by the pool or garden area. A nice Samual Adams or something big enough to stand up to a good cigar. I also like red wine and like a big Syrah or red wine blend. It helps I'm the wine business, so I have plenty of options.
Good luck with your choices!