How cheap can you go and still be happy with the sound?

Let's not be ridiculous. Good sound has a cost and it should. I don't think there is anything under $10k-$15k that would qualify.

And we wonder why the word "audiophile" has a pejorative connotation. This is just a tad elitist. One can "love audio" at any price point...there is no minimum buy-in to the club.

To answer the OP,. I've bought audio gear for my kids, and listened to various (factory) car stereos, and thought the sounds was "pretty good" and enjoyable.  Happy to have something to listen to, enjoyed plenty. 

That said, I still have issues when someone puts on satellite music - the compression is so clear.  Not as bad with MP3s streaming at reasonable quality - 320 kbps.

My higher end stuff is more fun to tweak and play with, but I think basic music enjoyment can be had with any gear where some quality effort is made by the mfr. 

@curiousjim

...try to keep music in my life as much as I can, because IT makes me happy!

Exactly. It's the music !

My first really good HiFi system limited by my budget back in 1977 was a Marantz 2270 receiver ($389 new), an Empire 698 TT ($375 new), MicroAcoustics 2002E cartridge ($100 new) and Infinity Monitor 1A speakers ($450 store demo’s). A very enjoyable system! Some months later I replaced the 2270 with an AGI 511 preamp ($430) and GAS Son of Ampzilla ($420) - both bought new at the store with the Infinity speakers. That was the start of my upgrade quest. Though if I had stopped there I would still be happy today!

IMO, this would qualify as a high quality (sonically) charity price hifi rig for any younger or older person w.r.t small room nearfield or midfield listening.

I am surprised that you have not repurposed a mansion somewhere so she could use that for her listening room.

I threw this together and turned out to be a killer el cheapie system:

yamaha a-s501 used $350

dayton audio outdoor IO8XTW speakers new $320/pair

pioneer blu-ray play new $350

AQ type 4 speaker cables $150ish

i listen to this strictly outside and is way more fun than my main rig.