There are a alot of options you can do to hunt elk. Outfitters that offer drop camps will pack you into good hunting country, and will have a camp set up for you. Once they drop you off, your on your own, wlthough some will leave a radio with you for check in or to have them come pack out your elk. They are $1-2,000 depending on the outfitter. This allows you a little more in gear weight. Call around and check references.
Another option is trying to hire someone to pack you in with your own camp gear. Again, research here is key, finding a packer in the area you want to hunt instead of hunting an area just because there is someone in the area who will do it.
For a DIY hunt,here are some estimates on costs for Colorado. If you are thinking of a different state, adjust accordingly.
For me from home in Michigan, we're talking about a 1600 miles each way. I'd guess from your area 2000 miles or so. You can figure your gas, food and coffee expenses from that.
The best thing about a DIY hunt is you can hunt as long as you want, vs. a typical 5-7 day hunt if you do a drop camp, or guided hunt with an outfitter. I personally prefer a minimum of 7-8 days, 2 weeks being great. If you can do it, take the whole archery season off.
Depending on how much you like to eat, figure food, and of course any personal gear you may want to take.
For me, based on $2.00 gallon gas, $500 for gas, $500 for tags, $250 for meat locker to process an elk if I get one, and food costs which vary.
The last time I went i flew out because it was a lot cheaper than driving. I had friends pick me up and drive to the ranch.
I'll PM you a suggestion for an outfitter thathas some great options.
But total cost for a DIY hunt can be around $1500-2,000. The memories of hunting elk in the beauty of the Rocky Mountains is priceless.