Best Bang for your Buck DAC ?

Love my RME , sounds great.....  its at that perfect price point where you get a lot for the money, great sound, etc....to better it will cost double. Nothing out there has its feature set.    Detail retrieval is excellent,  it has great bass, dead quiet, dynamic....works with any digital product.   Plug my iPhone into its,USB and it instantly recognizes it as a 768k/32 bit device.... same with my tablets, and PC.    Truly plug and play.

I view digital gear as " consumables" for lack of a better word.   Digital is  constantly evolving ,  I don't think I have the system to warrant a $4000 or $6000 DAC.... who knows, maybe something like the Bricasti DAC or dcs would elevate  my system to the next level. But  I doubt I have the associated gear to flesh out the differences.   Would be fun to try something high end in my modest system.

I think your instinct to go with Schiit is good. I helped a friend get his first high end DAC. It was a Yggi. In the process I bought a Gungnir multibit (for my office system). I highly recommend the Gungnir Multibit... it gets you close to the Yggi... all of which are simply screaming deals in high end audio. You would have to pay twice as much for another brand to equal the sonic performance. Check out the reviews.
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Just a word about really inexpensive DACs... you get what you pay for. Many years ago I poked around with a Dragonfly and a couple others... it was a complete waste of money for me. I finally bought a $4K DAC... holy cow... different experience completely. I made fun of Schiit a long time. Who would name a company that? But after extensive research and buying a couple... this stuff is the way to get into the high end.
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I recommend doing the multibit, in the long run stretching the extra $ is worth it. But if you can’t then the Gungnir is within your budget. It takes more than 200 (400) hours to break in... so it will sound good right away but not as natural and a bit flat until you get hours on... run music through it for the first month non-stopped and it will be broken in.

Or you could try an old classic like this that I bet sounds fantastic.
https://www.audiogon.com/listings/lisa9gb2-audio-logic-model-34lu-tube-d-a-convertor-da-converters

MHDT. Several models available

A excellent dac Black ice audio uses dual 12Ax7 vacuum tubes 
which I would put in NOS Raytheon Black plates 
brent Jesse audio, and a Synergistic 🍊 fuse decent power cord 
And beats dacs 2-3 x it’s cost .Underwood Wally sells them 
Retail $799,which you can buy for  less build quallity compact but very good especially the Rcore power supply Burr Brown dac chipsets. Rich involving sound ,even stock ,the tubes mentioned 
and fuse just add to the musicality and resolution .I started there 
then went much further modding it monies well spent IMO.