With the mechanical accuracy of firearms generally being superior to what people can actually make use of, 'accuracy' becomes a function of:
Sights (distant third place, but a possible factor)
The Walther PPQ has great ergonomics and a great trigger. For strict range duty, swapping out the sights is all that's necessary to have a fantastic system.
One of the best range guns that I have had the privilege of handling was an SA XDm 5.25" 9mm with a trigger job. That is easily in your price range.
Currently Own: Beretta PX4 9mm, Glock 23 (Gen 4), Glock 19 (Gen 4) x2