In addition to the ones mentioned before I would also suggest ENOTECA CAVATURACCIOLO a nice wine bar&shop where you can taste great Italian wines from all regions together with a large selection of Italian cheese, ham, salami and honey.
Norberto, the guy who is there is a great sommelier and a friendly person as well.He has a huge knowledge about wine and he's able to let you experience Italian wines at their best.
This nice wine bar is located near the car ferry terminal, at the bottom of the first stair after you pass the post-office which is located almost opposite the car ferry.

  

The second one it's quite well worth giving a go is BAR FLORENCE, actually the nicest and smartest bar in Bellagio.Here you can have some nice cocktails, sitting under the arcade, which are located a few metres far from the water.
Nice interiors and well-prepared cocktails make this one of the best after-dinner places, which I would recommend also for "aperitivo":the so-called drink Italian have before dinner.