Lungs, Legs, core and back. That's what I think you should focus on to get in elk hunting shape.
Lungs - interval running is the single best exercise I have found for my lung capacity. It is painful, but it works. Sprint on flat land for 2 minutes, walk for 2 minutes, do 8 intervals, you will be clawing for breath. If on a treadmill, put the incline on 5 or 6, run 6 or 6.5 mph for 2 min, then walk at 3.5 mph for 2 min. Do 8 intervals. You can't do this every day, on off days run 3 miles for time and try and push yourself.
Legs - The two best things I have found for legs are walking lunges first and foremost and ski squats second. As your legs get in shape, you can start doing walking lunges with a pack with weight to really get in good shape. Ski squats, put your back on a tree or a wall, go down till your thighs are paralell to the ground, start your stop watch. Do 1 minute intervals with 30 seconds of rest.
Back and core: General pushups and sit ups are good but I believe in practicing how you play. To that end, I have 3 20 lb sandbags I will strap those into my frame pack and go climb stairs. I climb for an hour, the biggest challenge is finding a building big enough, the one I climb is only 8 stories, so its a lot of up and down. I train with 40 lbs most of the time and do 60 only a few times to get a feel for the weight. You can also start with 60 lbs till you fatigue, drop to 40 till you fatigue, then do 20 till you can't climb any more.
The older you get the more time your body takes to recover and you need to incorporate that. When you are young buck you can't really over train, as you age you definitely need to give yourself some time to heal.
That's what works for me, I don't go in the gym, I just get it done on my own. One HUGE thing I never worked out with until last year is an mp3 player. Some good angry workout music keeps you going longer than you would normally. The other big challenge working out outside here is the summers get brutal. Climbing stairs in 98 degree august can be a real challenge.
I consider myself in elk shape when I can get a 40lb pack up and down 1000 vertical feet of stairs in under an hour. I live at sea level. Altitude is something you just cannot train for, but if you are in good shape it will take you 1-2 days to get acclimated, incorporate that into your hunt plans. The longest day I had last year was 17 miles about 5000 vertical feet in one day. It was a nutkick, but I survived and got up to go the next day.