So I am a college student that is about to graduate college in the fall, what state would you recommend me to start gaining points if I want a good elk hunt within the next 5-10 years with either bow, muzzleloader, or rifle?
AZ for elk but also put in for other species. You will be able to draw a decent archery elk tag in a decade but could be first year since have chance at random tag. In a decade is likely you can draw a December (early rut phase) Coues whitetail tag and this may be the most challenging mental hunt in the West.
Any other state is a crap shoot and, to be truthful, so is AZ. Cost will go up faster than inflation and tag allocation for non-residents is likely to fall compared to resident pool.
I would try NM as is a relatively cheap date at lottery odds where you are in the same crappy boat as a non-resident applicant that has been applying for decades.
After AZ and NM, the pickings get thin if only looking at a 10 year window. I would put UT next since they have some tags that go in random pass but you will not get enough points in 10 years to draw a great tag and if you do hit the lottery and get a great tag in the random then get ready for encountering false "private road" signs and hunters with 20 of their closest friends out zooming along on ATVs trying to get an elk.
WY has some random tags but the non-resident bucket gets sub-divided into two tag classes and then those divided into a preference and random bucket that most of the better deer units have no random tags and elk is not much better for random odds. If you had a 20 year window then would put WY right after AZ.
CO is an enigma. No random tags. The best units are decades of points now. You need to either buckle up for 30 years or hunt elk units you can draw with 10 or less points that might be a less crowded hunt than the OTC units but unlikely to encounter a mature, heavy antlered bull. If you primarily want meat then CO is an option.
NV squares bonus points so you do not gain leverage until are in the draw building around 16 points. At that point, you see your odds start to improve relative to those with more points than you. 10 years is not enough though are random tags so, like NM, a chance.
MT effectively is OTC with a long season so would consider MT if are looking at CO for OTC.
CA, OR and WA are terrible places for the elk game as a non-resident.
I don’t know about a good elk hunt as a non res in AZ every 5 years guess it’s what you consider a “good” hunt. I have 16 points in AZ for elk and have never drawn an early archery tag and I have never put in for any of the top tier units like 9 23 10 or 1 ..... Plus, remember the state can, and do change the way things are done mid stream no matter how many points you have and that can knock you backwards several years and then there is point creep.. I know a guy who has 9 points for AZ elk and two years ago he said he was burnt out on it and hasn’t put in since. Said he was done with it.
If you simply want to elk hunting go OTC Colorado or general MT. Don't worry about points. That being said, be prepared to get addicted and buy points in some states. I definitely recommend finding an every year or two type of place and then a state or two where you want to hunt in 5-10 years. AZ would be my recommendation.