More money toward better speakers or a better DAC?

I say it depends on what one has in one's system at the time of consideration.

In my case I was using a 10 year old DAC and had speakers that worked well in my room with my current amplifier. I wanted a new DAC, one that was NOS, R2R, and had tube output stage. Bought a Audio Mirror Tubadour III. It made a substantial improvement towards the experience I was looking for.  

OP, the way you pose your question makes it seem that you're looking for a prompt to go upgrade your DAC. It's your time and money -- and you could be guessing correctly, so why not try it? Otherwise, it's very hard to know.

On this forum, anyone can throw out the name of a component to swap out or a brand. The more important answer to your question would describe a process of elimination to help you identify where the weak link(s) are. Then, you could know if the speakers were the problem.

Steve Guttenberg has a good little piece about not changing your speakers too quickly. A lot here is old news to folks --how good is your power? is his main question, but he mentions other things, such as the DAC. https://youtu.be/7gXSvHDOjFs

There aren’t too many universal truths in this hobby as everyone hears differently and values different things, but two things I’ve found to be pretty universal are 1) everything matters and 2) the audio chain is only as strong as the weakest link.  Focusing on one area at the significant expense of another is not a strategy for building an optimal system IMHO. 

It is not always a case of drop a better component into your system and get better sound. The sound you achieve is a result of how all your components and your room play together. 

Unless you have an old DAC, it is likely that moving your speakers a few inches will give you a bigger overall change in your sound. 

But if you have already optimized your speaker positioning and like the overall sound... then trying a different DAC may be worthwhile.  Spending $3k doesn’t guarantee better sound than spending $1k... it’s what works/sounds best to you in your room with your other components. 

TUBADOUR III Non Oversampling Tube DAC,  interesting.

not sure what non oversampling dac means and what is special about a tube dac, unless it helps with treble/vocal sounds similar to a tube amp,