Colorado seems to make it easier for out of state hunters, especially for elk. Lots of public land. In most of the state it is possible to buy over the counter elk tags during the 2nd and 3rd seasons. If you want to bowhunt for elk the possibilities are almost limitless.
There is a drawing for deer tags and you need to apply before April 1. At least I think that is right. You need to apply for one of the better, more popular areas as your first choice, and a much less popular area as a 2nd choice. You will most likely get rejected for your 1st choice with no preference points, but selected for your 2nd choice. But you will build up a point. You need to build up at least 3 points to have a chance at a good area, but at least you will get to hunt. You can also just apply for a point, I think it costs $25. I have a BIL that hunts there every 3-4 years, but applies for a point every year. He only hunts when he builds up enough points to guarantee he'll be picked for a good area.
They also use a point system for elk to get into the prime areas, but it is much easier to just show up in about 2/3's of the state and buy an elk tag with no points. That is almost impossibe anywhere for rifle deer. Archery, yes.
The last time I hunted there was 2010 and deer tags were around $325 and elk $525 IIRC. The group I hunted with all applied for deer tags exept for 1 guy who decided to go at the last minute. When we got there they were sold out of over the counter deer tags in the area we hunted so it was an elk tag for him.
Check here for specifics, a few things could have changed in the last 2 years.
http://wildlife.state.co.us/HUNTING/Pages/Hunting.aspx
I had planned to go back this past Fall for elk, but was unable to find a partner to share the costs of the trip. It is a 3500 mile round trip from my home and a 28 hour drive to the area I planned to hunt. Too much driving and expense solo. When I went in 2010 I teamed up with a BIL and we drove it straight through sleeping and driving in shifts and split all expenses getting there. We met 4 other guys in camp who also helped share equipment and supplies. It is not too expensive that way. We spent around $700-$800 each for the whole trip including tags. Going solo I estimated my gas costs alone at roughly $800. Of course gas is also a bit more expensive than in 2010.