Oh yeah, you can definately do something within that price range. Id suggest taking a look at the various makers out there, watching for;
1, something shown as a Match barrel that is NOT chrome lined. Avoid chrome lining like the plague, it's pure death where accuracy is concerned.
2, something that is floated. These will usually be listed as Varmint or Match configurations, but the result's the same. Simple guide to AR accuracy; start with a good barrel, and float it. The rest is icing.
3, something with a good trigger. I like two-stage, but that's a personal preference. If you want to step into an aftermarket down the road, that's a better step yet.
4, figure out what other features you like, and look for those in the right combination. I'd suggest trying Rock River first, as I think they probably offer more models/options that will be in line with what you're looking for,
Take a look at their website, and see if there's any models there that jump out at you, and we can chat a bit more after that. Might also check the other makers as well, but Rock River is where I'd start.