With my Remington 750 in 30-06 I was able to hit a target about twice the diameter of a coffee mug from 100 yards away, so they're accurate enough.
Certainly good enough for most big game hunting at reasonable ranges, but any modern bolt gun should be able to do that easily.
However, if I was planning on spending $2K on a rifle, I would expect to be able, with first shot from a cold barrel, to hit a dime at 100 yards, and hit a nickle every time.
And plastic parts aside, I expect the Steyr is an excellent quality rifle, but I can not see it being worth anywhere near what they want for it. Maybe it is an exchange rate thing.
With your budget, for an off the shelf rifle I would look at something like this:
http://www.cabelas.com/product/REMINGTON-NA-RIFLES/1871671.uts or this:
www.cabelas.com/product/shooting/fi...5-finnlight-st-bolt-action-rifles/1774820.uts
If I wanted to spend a little more, something like this:
http://cooperfirearms.com/jackson-hunter or this:
http://www.cabelas.com/product/shoo...bolt-action-rifles-by-dakota-arms/1769624.uts
But most likely I would go the custom route mentioned above, because I can build exactly what I want.
You want a Kreiger, Lilja, Hart, Shilen or Bartlein Barrel, you can, in whatever length profile and twist rate you want.
You want a McMillan, HS Precision, Bell & Carlson, or a custom high-grade Walnut stock, you can.
You want a Jewell, Shilen, Timney, Kepplinger, or even the stock trigger, you can.