I have done many noise reduction details in my dozens of projects over the years. I am a master carpenter and licensed construction supervisor. I am not a specific expert in matters of sound deadening, but I have some experience in what works and what doesn't. The second half of the reply from Henry titled "noise reduction" is wrong because replacing drywall with homosote will really not make any noticeable difference. If you make a really thick wall there will be less noise, if you attached homosote to the inside of your wall there would be less noise (just a little less) - but these approaches don't get to the heart of the matter. Homosote shouldn't be used outside. It will turn to mush. It isn't too nice inside either. They sometimes use it for large bulletin boards in elementary schools. The commercial website that was in one of the other responses doesn't seem very practical for a do-it yourselfer.
Here is the real poop: Imagine your wall as having an outer skin (the siding and sheathing) and an inner skin (the drywall). They are connected acoustically primarily by the studs (2x4 framing members) and also by the space between the "skins". Sound is being transmitted outside and it is vibrating the outside skin like the skin of a drum. This gets transferred to the inside "skin" (your drywall) through the studs and the air etc. between the skins. This can be a fairly efficient process. We want to make in an inefficient process. What happens is that the inside skin then vibrates and transmits the sound into the air inside your house. Insulation between the skins can help dampen the sound. The thicker the insulation, the more dampening. I live in a 2x6 framed house that is quite quiet. It is noticably quieter than 2x4 houses or uninsulated houses. Also, I have double insulated thermal glass windows in addition to storm windows. The 3 layers of glass and 2 separate air spaces help a ton. So, going on the insulation principle alone, you could build a thicker wall with more insulation.
Assuming that you have insulation, another even more important way of transmitting the sound to your inner skin is directly through the studs. There are different ways to combat this. If you are building interior partitions in a new construction, one quick way is to use 2x6 studs and saw (rip)them in half lengthwise to within about 6" from either end. you then drywall both sides. In effect, you have built two walls. Another way of accomplishing something similar that will probably be good for you, is to create a new, acoustically isolated inner skin. What you will do is find some acoustic "Z" frame. You should be able to buy this stuff at any good home supply place. If they sell steel studs, they should have this. This is steel channels that you screw to your existing wall horizontally. The channel is sort of shaped like a "Z". You then screw your new drywall or soundboard (wood or drywall specially engineered for extra sound deadening)to the z frame. You use gasket or acoustic calking to fill the gaps and finish as a normal wall. A similar setup is shown on this page: http://www.tubetrap.com/DMP-DIA.HTM You don't have to use all of the pro studio stuff b/c you will achieve "good enough" results for a small fraction of the cost. Your situation sound kind of extreme, so if I were you, I would actually build an interior wall directly inside your existing exterior wall. You could use steel studs and plenty of insulation and z frame and drywall on the inner side. You only want this wall to touch at the top and bottom, even then, only where it is actually connected. You may want to use soft rubber bushings where your screws attach the top and bottom plate to the floor and ceiling. You also may want to use a piece of felt in between the steel studs and the z frame. A wood frame wall will work just as well as long as you use the insulation and z channel and don't touch the existing ext. wall. Leave a 1/8" to 1/4" gap all the way around the edge of the drywall and fill with acoustic calking. At this point your weak point will be any windows on that side. You can put on the outside a cheap storm window unit and maybe something else on the inside as well (not that cheap film they sell for winterizing, it won't help). Maybe just one solid piece of 1/4" plexi glass?
As for the underlayment for a tile bar top or any counter top, I have found that there is no difference between a solid particle board or plywood surface and any other wonderboard or other surface. Anyone who tells you you need a mudset or wonderboard backer must be over 50 or 60 when all they used to have was mudset jobs. This was a good idea before modern sheetgoods products were readily available, but wonderboard has nothing over anything else. I have built about 20 counter tops with tile over two layers of glued and screwed 3/4" particle board and I have never had a single problem. For this type of surface, it really doesn't even matter if you use a portland cement based mastic or the wall tile synthetic mastic. The portland based is probably stronger, but it won't matter because you won't have gorilla's dancing on it, you will have drinks on it.
Wonderboard is good for showers. It won't rot like green board or other stuff. If you, for some reason, MUST use it for your bar, it is a real pain to work with. The edges end up all ratty and if it gets bent then it is crumbly and weak. You would need to glue or mortar it to the substrate and fasten it every 8" with roofing nails or washer screws. It will give you no real advantage.