Planning a trip in June 2017 out west. We can fly either into phoenix, Salt Lake city or Las Vegas, depending on what is easiest for planning this trip.
We want to see the Grand canyon. Also do a one day raft trip that meets at Peach Springs Az.
Want to see Upper & Lower antelope canyon and take tours of each.
Bryce National Park
Zion national park (to hike the Narrows)
We will drive a full day from Salt Lake city to Yellowstone, seeing Grand Teton along the way & some other sights then spend a day or two in Yellowstone.
So is it best to fly into Vegas & do a route? fly into phoenix and do a route? We have no problem dropping the car at a different location if its more efficient.
My son wants to see The Arches but that looks wayyyyyy out of the way & not sure we want to make time for that. Any advice about route is greatly appreciated!!

The first information we will need to help you is how long of a trip this is. This is an ambitious trip plan but it can be done if you have a lot of time.

Bryce/Zion are close together are easily combined.

Yellowstone/Teton are close and easily combined (most people do combine, in fact).

Whatever your timing, it makes sense to move in one direction of you are really ok with a one-way car rental--you could do either direction
GC --> Zion --->Bryce Canyon --->Grand Teton ---> Yellowstone.

Flying into Vegas puts you in the middle so I don't think that's the ideal landing point.

I think Las Vegas makes most sense, doing a loop from there:

LV > Peach Springs > GC south Rim > Page (Antelope Canyons) > Zion > Bryce > GT > Yellowstone.

Hope you have a minimum of 2 weeks for this trip.

That is certainly the most economical route, MikePinTucson, since it won't include one-way car or air travel.

Looping around would be too much driving for me, personally, but it is a workable plan given enough time. Unless I were given about 3 weeks I wouldn't want to group all this together. But my driving tolerance is probably lower than OPs. I have done Zion/Bryce together and Yellowstone/GT together. I would never have considered combining all of them plus GC, though.

I know this isn't what you asked specifically but unless you have quite a bit of time for this trip, I would drop off Yellowstone/Tetons and include Arches/Canyonlands. I consider the Utah parks and the Yellowstone area two separate trips unless you are able to spend more than 2 weeks completing the trip. The Tetons are fantastic and really deserve more than a drive by. Yellowstone is usually recommended to give 3 or 4 nights at a minimum (more is better) and you can add on to that to see Cody/ Beartooth Highway, etc.

If you just focus on Grand Canyon/Page/Utah you can make a really great trip without the long drive over to Wyoming.