The '06 is such a versatile cartridge, such that it's fine for medium range shots on Antelope, Deer, Elk, or even Moose.
I have both an 06 and a 7mm Rem Mag and love them both. I feel more comfortable hunting fields where 200+ yard shots are possible/likely with the 7mm. In the woods or in small fields I'll take whichever I want to take. For all practial purposes, the big 7 shoots as flat as a 270 (a .270 is a 30/06 case necked down to take a .277 bullet, about 0.03 smaller than the 30 caliber (.308)) that hits as hard as the '06.
You could go smaller, such as the previously suggested 25-06, .243, 257 Weatherby Mag, etc. Each of these calibers (especially the larger powder charges of the 25/06 and 257 Wby) would be great for antelope and long range deer hunting. The 25/06 is a 30/06 case necked down to .257, similar p owder charges as the '06 and .270 only with a smaller diameter and lighter bullet. Usually the 25-06 stays in the 100-120 range, the .270 in the 130-150 range, and the 06 in the 150-180 range on bullet grain weights.
However, if you do go smaller, you limit what you can do when it comes to how far you should be shooting at stuff with the bigger '06.
If you go bigger (7mm is such a small increment bigger than the 06....then you should go WAY bigger), such as a 300 magnum (winchester, weatherby, Remington Ultra Mag), or .338 mag (Weatherby, winchester) or split the middle with the 325 win short mag, then you get longer range killing power on bigger game such as elk/moose -AND- if you're going to be reloading, you can get 150 grain bullets on those big 300 mags and REALLY reach out and touch an antelope.
Of course, what you REALLY ought to do is just check out some ballistics of popular factory produced ammo and see what types of ranges they appear to be competent killers with. THEN you ought to do a quick search at (
www.gunbroker.com -or-
www.gunsamerica.com) or even at
www.walmart.com and see if you can find any type of rifle that you're comfortable with in price/style/action (whatever) that are ALSO chambered in one of the calibers that you think would benefit you're gun collection such that you could either hunt a different set of game with the new gun -OR- hunt the same set of game in different fashion (prepared for longer shots, whatever).
I love ballistics of the 300 Weatherby (and the 300 Rem Ultra mag is awfully similar) and view it as a longer ranged and harder hitting 30/06, but that's just me AND the fact that guns chambered in the 300 weatherby kick ass (Mk V and Sakos).