happytohunt,
You've got some choices, and decisions to make, for bighorns. If you aren't picky and it can be either Rocky Mountain or California Bighorn then more opportunities are available.
Know that drawing ANY Bighorn tag is like winning the lottery. You'll also probably need a bit of a "fund" to deal with applying in the draws (for those states that require putting the fees up front to be in the draw) and/or a credit card with a credit limit high enough to deal with the hit of the tag fee after a given drawing is completed.
You can apply to draw a Bighorn tag in the following states: Washington (there is also at least one raffle tag available) - both California and Rocky available, Oregon (also one raffle tag available) both California and Rocky available, Idaho (also one raffle tag available) - both California and Rocky available, Nevada - both California and Rocky available, Arizona - Rocky, New Mexico (also one raffle tag available, though it is sometimes for a Desert, depends on which species the auction hunter chooses to hunt in a given year) - Rocky, Utah - Rocky, Montana - Rocky, Wyoming - Rocky, Colorado - Rocky (also one raffle tag available), North Dakota - California subspecies.
You might find the information posted on the Grand Slam Club / Ovis forum helpful. It's got both draw and raffle info posted (I post much of it and just don't care to repeat it on multiple sites:
http://wildsheep.org/groupee/forums
You can also find information on Dall sheep outfitters there as well:
http://wildsheep.org/directory/grand_slam_advertisers.htm
Hope this helps a bit.