Asking "What is the best gun for concealed carry?" is like asking "What is the best car to go fast in?"
You need to add some criteria. What kind of experience do you have? Where do you plan to carry it on your person (inside the waist band, pocket, ankle holster, etc.)? Does recoil bother you? Do you prefer pistols or revolvers? Etc.
Personally, my vote goes to the Smith & Wesson Bodyguard .380. It's small enough for pocket carry, slim, has a safety (my preference), is DAO (no hammer to get caught on the pocket lining), decent sights, and holds 6+1 rounds of .380. .380 is no powerhouse, but it packs enough of a punch, unless you're planning to go up against bears, mountain lions, or the Incredible Hulk.
For something with more stopping power, it's a trade-off with size and weight. My next purchase is most likely going to be a Smith & Wesson M&P Shield in 9mm. I have carried a full-frame 1911 and a service-size double-stack 9mm before, and they're not fun to conceal. Even my Bodyguard in an IWB holster gives me more issues with everyday clothes (jeans and T-shirt) than just sticking it in a pocket holster. I hate having to worry about whether or not my shirt rode up and flashed my gun to anyone around me when I bend down to get an item off a bottom shelf.