Software for Room Correction?

There are a lot of options here. As for a mic the most popular options I’ve seen and used are the MiniDSP UMIK-1 and the Dayton Audio mics available on Parts Express. 

What are you using for your digital playback chain? Are you using a laptop/computer direct into a DAC or preamp? If so you can use REW (Room EQ Wizard) which is free or Dirac Live. If you have a streamer/server you can look into a number of DSP solutions with room correction, like MiniDSP. 

If you can list the components in your system you will get better guidance to the quality of the DSP solutions that will best match it. 

I use an Innuos Zen 3 Streamer

Uptone Audio Etherregen

An ANK 4.1x DAC

Pass Labs INT25

Fritz Carerra 7BE Speakers

REL T5X Sub

Balanced Power Transformer

Truth be told I experienced this effect recently

with a pair of Buchard S400 Mk2s at someone's home.

They went from Okay to Jaw dropping.

 

Maybe my jaw dropped because I knew how they

sounded in two other rooms and was shocked by the

improvement.

What gear were they using?
Finding out what your acquaintance was using would be where I would start.

So who uses this gear and what do I buy???

Your choices are a built in unit that does a lot for you, or a unit that has more of a DIY approach for tuning.
And at a kindergarten level, one has choices of more of a PEQ approach for frequency response, and more of the DIRAC for phase correction.
So there is a bit to consider.

Some ideas/examples to bound the field include:

• MiniDSP FLex using DIRAC
• Lyngdorf TDAI 3400 integrated.

With an integrated amp it might get harder, as the DSP usually sits between the preamp and the amp.
If one only has a digital source then it could sot between the DAC and integrated.
i.e. :

Balanced Power Transformer

I use an Innuos Zen 3 Streamer

Uptone Audio Etherregen

An ANK 4.1x DAC

It probably needs to go here for a full spectrum solution.

Pass Labs INT25

Fritz Carerra 7BE Speakers

But it could go here for a sub correction only DSP 

REL T5X Sub

I would probably suggest you just get the microphone and REW. You will need the same UMIK mic for many systems (like all the MiniDSP), and a lot of processors that do it for you come with their own microphone… but having a mic is not a bad start.