[TKonrad.NOLA]

.....would be great if it were ≤ $1500.  I am using a VPI Scout Jr and about to upgrade to the  Scout 1.1.

[audioguy213]

It is much easier to find MM than MC,
Rogue Audio sphinx v2 is well regarded.

Options open up used,  but phono in integrateds is getting harder and harder to find.

For an excellent, cheap solution, if you like you current amp, try the Schiit Mani - it is a $129 SS phono stage, that simply does things properly, it will not let you down. IMO.

I have not heard it, but Rega Brio - R gets some love on the affordable end.

[S Clark]

A good friend had a Sphinx... liked the phono stage, didn't care for the amp.  It's been long gone for a couple of years. 

[Wayner]

The new Yamaha integrated amps are suppose to be pretty good....

[ACHiPo]

Have you considered vintage?

[neobop]

You might want to remain flexible.   This time of year you'll find deals on good equipment.   
The features you're looking for in an integrated (remote control?), might have no bearing on a phono stage. 

Example - I just got a summer clearance brochure from Music Direct.  They have a Simaudio Moon 110 LP for $400.  There are some nice phonos in the $300 range - like Vista or Lounge.  I suspect there's a wider selection of nice integrates w/o phono and you could upgrade or change one without the other.
Used stuff is a nice way to get higher end equipment.

neo

[Doublej]

Perhaps below your price point...

https://emotiva.com/products/amplifiers/pres-and-pros/ta-100

[md92468]

I have no personal experience with this amp, but I've read lots of raves...slightly out of your price range, but might be worth a stretch:

http://store.acousticsounds.com/d/88038/Croft_Acoustics-Phono_Integrated_Amplifier-Integrated_Amplifiers

[Doublej]

Coming soon...

http://www.peachtreeaudio.com/nova300-amplifier-with-dac.html

[gnostalgick]

  I'd also recommend checking out the Croft Phono Integrated, based on my experiences with his Micro 25 pre.  (I'm also pleasantly surprised someone else mentioned it first.)  I'd consider my Croft the most over-achieving component in my (modest) system. Admittedly, my sources are all digital (much as I'd like a decent turntable, its not currently in the budget), but others have said that Croft products should be considered as high value phono stages with a quality pre &/or amp thrown in for free.

A few reviews here:
http://www.stereophile.com/content/croft-acoustics-phono-integrated-integrated-amplifier#WAffr9QX7ImMdVrC.97

[ACHiPo]

  I'd also recommend checking out the Croft Phono Integrated, based on my experiences with his Micro 25 pre.  (I'm also pleasantly surprised someone else mentioned it first.)  I'd consider my Croft the most over-achieving component in my (modest) system. Admittedly, my sources are all digital (much as I'd like a decent turntable, its not currently in the budget), but others have said that Croft products should be considered as high value phono stages with a quality pre &/or amp thrown in for free.

A few reviews here:
http://www.stereophile.com/content/croft-acoustics-phono-integrated-integrated-amplifier#WAffr9QX7ImMdVrC.97

Looks promising.  Art Dudley's been a reliable reviewer in my experience.

[gnostalgick]

Hey, did you find an amp yet?  There's a Croft on Agon for $1100, if you're still searching.

[johnto]

Check out the Parasound 2.1 halo integrated great sounding phono section mm and 2  mc settings. If you're lucky ypu can hit on a used or demo . Awsome
Sound power and flexibility.

[stevoz]

Vintage Luxman or if the amp is new, go with a decent separate phono stage, they're usually better than integrated phono outputs.