A-Caroling We Will Go

Gaudy Winter Veil Sweater
Use this item in Orgrimmar, Thunder Bluff, Silvermoon City, and Undercity.
It is possible to enter each of these cities without dying or aggroing any guards, save Silvermoon City where you cannot fly and there are guards posted at the only entrance.

Also please for god's sake stop downrating this for the content of the replies. There's a button on the replies for that.

EDIT:Scuttler's Shell will enable you to complete Silvermoon without aggroing any guards, and will actually allow you to get fairly deep into the city as well.

Oddly enough, this isn't the first time someone has wanted to kill me for singing.

This route should work for getting it as quickly as possible (assuming you have your hearth in Stormwind):

From Ironforge, take a flight path to Shattered Sun Staging Area on the Isle of Quel'Danas. There is a warp jump after you fly out of Ironforge to QD. Then when you land take another flight to Zul'Aman. If you fly direct from Ironforge to Zul'Aman, you go the long way, all the way up the coast.
Ride to Silvermoon City. If you bring a water walking potion or two, you can ride up along the lakes and rivers at the eastern edge of the zone. Just make sure to avoid the small outposts with the large guards.
Ride through the gates of Silvermoon City. After you get killed by the guards, it may take you one or two more deaths to get outside their aggro range, inside the city. The guards at the cities aren't the level 90 super guards, so you may or may not be able to take care of them. There is a nice gallery near the front entrance that you can rez in, that should be outside any guard aggro range if you're level 85. Do your song.

If you do manage to get killed, be careful about spirit rez'ing. As I recall, the graveyard you rez at is inside aggro range of the guards at the small outpost there.

Ride back to Zul'Aman, and take a flight to Andorhal in Western Plaguelands. Fly to Undercity. Make sure you are in a zone that says Undercity, the courtyard and several other aboveground areas don't count. When you get flagged for PvP (on a PvE servers), or if you open your map and it shows the Undercity zone instead of Tirisfal Glades, you're in the right place. Flying down into the actual city through the side entrance shouldn't be necessary. Once you've done your singing, you can hearth back to Stormwind.
Take the Cataclysm portal from Stormwind to Mt Hyjal. If you have epic flying+ you're probably better off flying directly from Mt Hyjal to Orgrimmar. The flight paths out of Mt Hyjal are mostly on long looping indirect paths. Once you've done your singing in Orgrimmar, fly on down to Thunder Bluff, and you're done. While you're in Thunder Bluff, you can just land in the valley between two mesas and sing there, you don't have to be up in the city proper.

Or, as has been pointed out, you can take the zeppelin from Undercity to Orgrimmar. I find landing all the way on top of the bag works well when I'm riding Horde zeppelins. The zeppelin to Orgrimmar has the red Orgrimmar banners at the landing, so you can be sure you're on the correct one.
You can do your singing without even leaving your ride. There is a zeppelin that runs from Orgrimmar to Thnderbluff as well, but I think a flying mount is probably faster than hanging around Orgrimmar dodging guards and other players while you're waiting for the zeppelin.

You may want to wait a day or two before doing this, there are sure to be hordes of griefers trying to interfere with people trying for this achievement.