What are the DACs that use good circuits in the Audio sections?

Confused about your question but yes many have good analogue stages. For Example Modwright Elyse is built on a PCM1794 and has a tube analogue stage after conversion.  
Here is photo:
http://www.modwright.com/cms/resources/elyseint-w1000h680.jpg

chips, a concern?  Well, that is up to you.  I assume that if chips were SOTA, then Audio Research, Conrad Johnson and more would have pre and power amps that were all really big chips. 

 Chips/I.C. etc.  are in the ear of the beholder. 

I don't know of any DAC that doesn't have a chip or PCB in it. 

ARC preamp have chips in them to run switches, drive display, count tube hours... as do many many others including Aesthetix, the display is defeatable via the remotes for clearly better sonics. The Aesthetix Pandora DAC has an IMO stellar analog output stage ( as does the Lampizator... I own both )....

To make it a bit more clear, I am not talking of Chips/etc. in the units other operating parts, but in the audio signal path...what you hear, not what makes the display work.