Agree with the production like quality slip on the Remington 700. However, that does NOT apply to Custom Shop. If you can step up a bit, you can get a really nice Remington 700 with blueprinted action, air gauged barrel, nicely adjusted trigger with no creep or overtravel, and with a good wood or synthetic stock, accurately bedded. Custom shop workmanship is much better than the assembly line.
For over the counter production rifles, the current generation of FN Winchester 70's are nice, as are the Browning A-Bolt and X-Bolt rifles, both with very accurate barrels.
Savage makes incredibly accurate but homely looking rifles. The Ruger American is developing a nice reputation, but it is very plain also.
Weatherby Vanguard has great value. The Mark V action is superb. Styling is not for everyone, but I love my Mark V 300 Weatherby.
I do agree that for deer hunting at all but extreme ranges, there are a lot of highly accurate rifles out there that are reasonably priced.
Frankly, the best value is a used Remington 700 from the late 60's through the 80's. Remington still cared about quality on its production floor and parts and accessories and upgrades for the 700 far exceed anything else out there. That's where I would begin in looking for a deer rifle if I did not have one. Get the seller to agree to let you have a gunsmith check it out before you buy.