Good Entry-Level DAC

So I had a nice California Audio Labs (sort of ) tubed  DAC that I used with my Rotel CD player. It ,made a huge difference to the sound; after getting it, I re-discovered my CDs! 

I moved over to a NAD C516 BEE CD Player (I know, entry level, but that's what I've got) a couple of years ago or three. I found the DAC didn't make any audible difference; so I sold it.

I think the NAD has a pretty good DAC Chip ( 24/192 Cirrus Logic Delta/Sigma DAC, whatever that means). Is there a reasonably priced ( < $1K) DAC that could significantly improve the sound?

Ideas, anyone? 

gasbose