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

There is no way to avoid a "chip" altogether.  Something has to do the processing.  That being said, Chord and PS Audio use a combination of hardware and software in the decoding process.  Chord chooses not to change OS through time, but PS Audio change OSs all the time which does have a distinct impact on the sound of the DAC.  These would likely be the closest to what you are talking about as they are not dependant on ESS/Cirrus Logic/Wolfson/Burr Brown chips you are talking about though other DACs don't use them as well.  

I personally had owned a PS Audio DSD with Bridge II for a long stretch and was quite happy with it.  Only sold it when I became a Chord dealer and now I use different Chord products at different times.  Both companies make superb products.  

Lampizator with a tube output stage is a good choice! Expensive, though!

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.