How to make use of Skull Built-in Audio

I have tried my Pyle Sound Box Splash (PWPBT60) with my Skull Canyon PC, sounds great from light acoustic Heart songs to deep bass Tool songs. The Skull Canyon sounds as good as any other source I've paired it with, so I don't think your NUC is the issue.

I'm probably stating the obvious here, but it sounds like the issue is the speaker you're using, not the NUC. Skull Canyon has excellent audio output, but the quality of the speaker will determine how much of that you hear.  There's no "best" speaker to use with the NUC, any more than there's a particular speaker to use with any computer.  I've used numerous speakers with my NUCs, both wired and bluetooth, and there's a huge range of sound quality out there. As you point out, with the bluetooth speaker you're only getting mono output, so it's not going to sound as good as stereo headphones. Looking at it from the link you include, it looks like a very basic, inexpensive speaker.  In this case, you get what you pay for.  I know it's hard to know what a speaker will sound like when you're buying online, but you can't expect much for that price.  I'd suggest heading to a store that sells speakers to listen to a few (possibly using your phone as the audio source) to see what works for you.

The short answer is, it's not the NUC, it's the speaker.

And as well as needing to choose a speaker appropriate to your needs, bear in mind that the bluetooth standard compresses audio. So a speaker connected to the NUC via a cable will sound better than one connected via bluetooth.

Yep, forgot to mention that.  In any case, bluetooth speakers tend to be hit & miss. I've had some that sound pretty close to a wired connection, and I've had some that are downright awful.

These were surprisingly good, especially given the price: Amazon.com: Bluetooth Speakers - August MS515 - Wireless Two Unit Stereo Set,Black: Cell Phones & Accessories

I am also using an Asus VE278Q via HDMI and Display port and I get good audio from the monitor speakers.

https://www.asus.com/Monitors/VE278Q/

I just need to make sure the HDMI sound is enabled through the monitor menu (configuration) and I select proper playback device
http://www.digitalcitizen.life/how-change-default-playback-recording-audio-device

NOTE: This link is being offered for your convenience and should not be viewed as an endorsement by Intel of the content, products, or services offered there.
 
Allan.