Best options for active speakers $4k or below?

Want a simple but superb sounding all-inclusive active speaker for my elderly but loud-music-loving mother in NJ. Used is OK!

Focal works.  Well priced for performance.  Easily found and returned.
If you like the idea of extreme clarity, resolution, and dynamics, I too recommend trying the ADAM S2V's.... I've got the S3H's, which are 3-ways.  They have a digital crossover, and parametric EQ available to you, if that appeals to you.  Many audiophiles don't like that sort of thing.   I love them!  I like the ADAMs better than the Focal studio monitors, although Focals are very nice, and more attractive.  These are not lifestyle speakers with Bluetooth.  They are studio monitors.    
If you have some serious power, Magnepan. 
I'm running a set of highly modified Yamaha HS-80M monitors on my computer audio system.  I have tested these in my home theater system and they actually are very respectable for a far field monitor, so don't necessarily think that all studio monitors are strictly for "near field".

I have the Adam A77x on my future list for an upgrade from the Yamaha's.  Even though they still use Class D for woofer/mid, they will use a Class AB amp for the tweeters.  Also, they have a higher extension ribbon type tweeter.  I like ribbons better than most metal dome tweeters that are popular in other monitors.  In addition, the A7 line still uses linear power supplies for amps.

The S2V that I recommended is a step up, but it does convert the analog inputs to digital for the internal DSP/EQ.  It's great if you need EQ for slight room correction.  However, the slightly cheaper "A" line might have better transparency.
+1 on Devialet Phantom. Can fill almost any room.