Where is the best place for the ERA 300 speakers in my living room?

Guessing the Arc will be high mounted, above the shelf over the fireplace? 

On the back wall, below the vents and as low as possible would be my 300 location.

The Sub will be interesting in that space too. Possibly next to the doors on the left where I think I see an outlet. At the front, flanking tne fireplace might work, have to watch the heat though. If you find you need two Subs, a possibility in that big room, the flanking option looks even better.

Yes, the arc will be on the shelf above fireplace. Also wondered about the sub placement. 

Use a quality surge suppressor power strip centered between the ERA 300 surrounds.  Hopefully they will both reach the power strip.  My 300s are on stands about 7 feet behind me.  If they are too close to the listening position or too close to walls they will not meet their full potential.

I would locate the Sub to the right of the TV on the floor.  That’s where the bass viols are.  Of course if you don’t listen to classical ignore that advice.

That vaulted ceiling is going to have a negative effect on the height channel reflected sound.  May still sound OK.  I would definitely tame that hard floor.  If not you’ll have some very long reflection issues.

We got our floor reflections under control with some thick wool carpets, without them the room was way too live.

Didn't need a lot to the sides other than the insulating curtains over our glass doors.

Aside from the carpet any other accoustic treatments should wait until you hear the completed room for a while.

Edit, maybe try the 300s inverted to keep the vaulted ceiling from eating the height channels. 

We’ll definitely have a large carpet and a large couch to help with reflection. Do you think even inverting them if they’re mounted by the vents would be a good idea or just something to play with during install? 

With the high ceiling the upfiring drivers may not be loud enough to drive the desired sound field if bouncing the sound.

By aiming them down, and as high as they will be, you should get enough height sound energy to your listening position Also, they are going to be high enough to properly position the height channels when inverted.

I'd really lean to inverted and low under the vents as my preferred option.

You could mount them higher but they are already going to be a bit high for the sidefiring drivers which seem best at ear level.

I’d think, with a vaulted ceiling like that, you’re not going to get much ‘Atmos’ effect out of the upward firing speakers on the Arc Ultra anyway. As suggested by ​@MoPac already. 
 

My ‘vault’ is much less, but certainly impacts my setup. I’ve given up messing with it, 98% of what I watch/listen to isn’t in Atmos anyway, it just isn’t worth the effort, much as I want ‘perfection’. It handles Dolby Digital quite well, though, and I do love the Era 300 surrounds. Mine are on stands, at ear level. 

It seems like the consensus is I won’t be chasing perfect, but instead I’ll be chasing the best sound with the most functional set up and most importantly what my fiance thinks isn’t an eye sore. I’m leaning towards mounting them below the vent and getting mounts that allows me to invert them and I’ll mess with the orientation once everything is setup. 

Any other feedback is greatly appreciated. Was in the living room today and it seems like the only spot for the sub is to the left of the tv because of that the only place there’s an outlet close