Leaning heavily towards the 30-06 and possibly the .270 or .308. Any thoughts or suggestions?
You really can't go wrong with either.
The .30-06 and .308 are similar in performance, with the 30-06 having a bit more power, but at the sacrifice of a longer action. In addition, the .30-06 also has a bit more recoil, but nothing to be worried about. The 30-06 also has a wider range of available factory ammo, and can handle bullets larger than 180 grains better than a .308.
The .270 is, of course, an excellent cartridge in its own right. Only problem here is that bullet weights generally range from 130 to 150, whereas the .30 calibers are 150 to 220.
Hunting black bear, especially at closer distances, does not require a cannon. Same is true for elk. As such, the .270, with premium bullets can work just fine. However, the .30 calibers are, in my opinion, a better choice for black bear and elk.
If I had to chose between the three that you mentioned, then I would select the .30-06.
Zachary