good integrated amps that don't include a phono section or a DAC

Rega Brio-R

Has the Phono but i don't use.
I have the 2007 version and I absolutely love it.

I don't think you need to look for something that absolutely doesn't have a phono or DAC.  Sound quality should be your main concern.  Here are a few integrated amps that come to mind around the 1k price point new with wattage and some comments (in no p-articular order):

-Arcam A19 (50wpc, recently discontinued, smooth sound, has phono)
-Rega Brio - (50 wpc, new model recently, has phono, well reviewed)
-Musical Fidelity M2si (new, haven't seen a review, around 75 wpc)
-Yamaha A-S801 (100 wpc, good clear sound, phono and DAC)
-NAD C368 (80 wpc, Class D, DAC and Phono
-Creek Evo 50A (55 wpc - no DAC/Phono, good reviews)

Those are the ones that pop into my mind right now.  

If you don't mind used a Naim Nait5i sounds great (owned one and miss it). Rega Elex R used can be found for around 1k +/-. Wonderful amp. You have some nice recommendations above as well.

I have an Anthem 225 integrated and am very happy with it. Phono is built in - no DAC. Plenty of power and control over any speakers I own/ have tried.

Used should be within your budget.

Regards-

Used Hegel H80 is under $1k.   Its internal dac can be bypassed I believe.