You' ll find an advocate for each of the calibers here, I' m sure, so I' ll just try to give you a rundown of my impression of each.
.30-06 I' ve never really liked. Maybe because it' s too popular.
The thing is with that rifle that you can load up or down as you see fit - all the way up to .300 Win Mag ballistics with Hornady Light Mags. It' ll shoot pretty flat.
.270 is, for my money, the best option here. It shoots very, very flat, and is great poison for any whitetail. It' s almost as popular as the .30-06, without the capability to load it heavy like you might want to.
.308 is, as somebody will tell you, the caliber that a lot of military snipers use. As accurate as you' ll find, pretty decent ballistics... not my cup o' tea, personally.
7mm Rem Mag is the most firepower for your buck on the list. If you think an ' 06 is on the high side for deer, I wouldn' t go there. It' ll shoot as fast and as accurate as any gun on the list, and have more speed to spare. It kicks like a mag, though, and... well, again, if you' re looking to go ' less gun' from the .30-06, I think you' re looking at the wrong rifle.