there is roughly about as much difference between the 7mm remington magnum and 30-06 as there is between the 30-06 and the 270.
All 3 would be fine. Going a bit lower or a bit higher would be fine too. Of course, an inch here or there...that eventually adds up.
the 7mm remington magnum has a superior trajectory aided by a higher starting velocity and a more areodynamic bullet.
It also has more recoil and the ammo costs more.
Nothing wrong with stepping down to a 30-06 for lighter recoil and cheaper ammo.
Of course, nothing wrong with stepping down to a 270 winchester either, even softer recoil.
Obviously you can eventually give up enough inches here and there to get yourself into a less desirable selection. I think if you take another step down to say 25-06 while it will work okay for elk,you are loosing something at that point.
In the same manner, if you keep on stepping up, many folks find out that the 300 winmag is just a little more recoil than they can handle.
The 7mm remington magnum seems to sit at the top of the 'ideal balanced cartridge' for elk, while 30-06 sits in the middle and 270 sits in the bottom of that same window.
But anything in that window would be fine.
Two more items for consideration. 7mm remmag is enough bigger that you generally have one less round in the rifle. Second, most manufacturers tack on an additional 2 inches to the end of the barrel for their 7mm remmag and 300 winmag rifles, this means it is generally a bit closer to the numbers you see on ballistics tables, while the 30-06 in hunting rifles often falls a bit short of what the tables would indicate. Normally those tables assume all guns are using 24" barrels.