What's the best integrated amp in the $1500-$2000 range?

Peachtree Nova 150. Been using it for a few years and it is good. For the price maybe great. You can get one for under a $1000.

Rogue Audio Sphinx V3. Brand new, it may be the best, in that price range.

Isn’t there a separate form here for amplifiers and preamplifiers? If so, there you might find additional expertise more directly related to your question.

Used Rogue Cronus Magnum II around 1500$ will drive most of speaker well.

Actually you have to specify your speaker since synergy between amp and speaker is important.

I've owned many integrated amps over the years, both tube and solid state, from the following companies: Plinius, Bryston, Arcam, Anthem, Rega, Peachtree, Cayin, Antique Sound Labs and I'm sure there are others I've forgotten. Out of all the integrated amps I've owned, my favorite is my current integrated - the Rega Elicit-R. It has plenty of power to drive most speakers (is driving my 4 ohm speakers with ease), is a musical, full sounding amp with great bottom end, and it has a really decent MM phono pre-amp built in. There is one on AudiogoN right now, listed at $1500. If you can get away with a little less power, there is the very similar Rega Elex-R listed here for only $980. That is a great bargain IMHO.

Unless you plan to buy a relatively expensive separate phono pre-amp, having a decent one built-in is a good way to go. Saves you money on interconnect cables, power cord and the price of the phono pre-amp.

Good Luck. I hope you find one that makes you happy.