Although prices on all guns appear to have gone up a staggering amount (I say appear because I believe it's actually all due to inflation) I guarantee you could get a very accurate 1911 for far less than 1500$.
At the last gunshow I went to, the SA 1911's I saw going for about $600-650 7 years ago were all around $800-850.
I think you can still find deals like this:
http://www.gunbroker.com/Auction/ViewItem.asp?Item=115084685
- if you are willing to buy something "like new" instead of brand new.
As far as accuracy - I can shoot 12g casings off a fence at 20yds with my 1911, and I believe I could do the same with any 1911 that was made by a good company, no matter how basic a model it is. You just have to avoid the companies that are putting out junk, like Charles Daily and the cheap foreign made copies like the Llama you mentioned.
I think USA-made Springfield Armory stuff is the best quality for the money.
However, one thing I would stay away from is their GI spec 1911's. They shoot fine, but they don't have the nice beavertail grip safety, the extended slide safety, or features like a skeleton hammer, adjustable trigger, beveled mag well, etc, all of which were fairly standard until this rash of GI specs came out a few years ago. I don't really understand what the craze was all about - all those features were added onto the original model for a very good reason.
Before I blab on any more about 1911's....does this mean you're willing to look at .45acp? I personally prefer it, but if you're sticking to .40, you have a much smaller selection as far as 1911 "style" guns are concerned.