(1) Within the AVR arena at your suggested pricepoint strata, there are numerous brands thst will be a step-up in audio performance from your NAD. ARCAM, CAMBRIDGE, and ANTHEM AVRs are the first three contenders off the mark .... Google the reviews....better still go audition them.
(2) Without prejudice to anything immediately above, a quality Euro-build 2-channel integrated amplifier at the same comparative price point strata will easily best any AVR in audio performance .... full stop.
The degree of audio performance improvement in a quality-build integrated over an AVR will not be subtle.
The list of available suitable integrated amp contenders at the $1,000-ish (+/-) price point strata is a long one.
IMO sell your NAD AVR and move on if you are seriously planning an integral step to improve your 2-channel audio performance.