The Montecristo No. 2 is a fantastic Cuban cigar. Also try the Partagas series D no. 2. These are not "mild" but they have a great taste. Vegas Robaina is a very mild Cuban smoke, IMHO.

I've never heard anything about Cubans containing "weed", so I don't think that's a problem. You realize, of course, that Cubans are illegal to possess by an American. You might want to be discreet about having them around your superiors. That being said, your superiors probably have a stash of their own!