First of all congrats on the tag. You will love this hunt. I would start by driving out of Cody WY on HWY 120 towards Clark WY. Turn left off HWY 120 towards the town of clark and stay on that main road until it turns to dirt. You will then be in goat country. I have found most of the goats to the north of the road. It is very steep and we have passed on tremendous goats because we could not reach them. Next check out clarks fork canyon by taking HWY 120 out of Cody and turning onto Chief Joseph HWY. You will travel for several miles then be in excellent goat country. I have killed 2 goats with buddies to the east of the HWY. There is a ton of country to glass and my advice would be to not shoot the first billy you see. Good Luck!!
The first attachment is the dirt road that comes in from clark WY. The road ends in a parking lot and there is a trail up the canyon from there. The other is HWY 212 on the Chief Joseph HWY. The canyon in the middle is a hot spot and everyone overlooks it. I saw a 9" billie there last year on my way to my Montana unlimited sheep hunt. If you hit Beartooth lake you went too far. Good luck and keep us posted!