Taking the family for a camping adventure out west later this year. Going from Ohio to the Grand Canyon up to Yellowstone and back. I'd like to take the D750 and 1 lens (to avoid over packing and keep it simple).

I'm looking at getting a 24-70 2.8 to use while traveling as well as to have in my lens collection. I currently have a 50 1.8, 24-120 f4, and a 70-200 2.8.

I'd like something with a little zoom and the versatility of the f2.8 for when we are back home. Suggestions appreciated.

24-120 seems like the obvious choice to me.

I would take the 50 and the 24-120.

24 - 120 does seem like a great choice.
I've been pondering an Olympus (2x on M43) 12-100 as a travel lens. Same basic idea - wide angle to telephoto without changing lenses.
On my Canons it would be the 24-105 L or 28-300 L to fill the slot.

I really like my 24-120 f/4, if I had to go with one lens, that would be it.  For me, I'll take the longer 120mm focal length over the 1-stop advantage of the 24-70.  [D850 is my primary body]

But, Yellowstone?  I'd bring my 80-400 f/4-5.6

This was a lens I didn't have in 2021, but wish I did.  I was out west on a climbing trip, a climb that almost didn't come together, and had I not been able to secure a climbing guide, the money not spent on that was going to go to buying a 200-500 back here at a local shop at home, and have them ship it General Delivery to some place between Denver and Yellowstone, and really focus on spending time in Yellowstone that time.  

With just a 70-200 f/2.8, I just don't think it's enough lens for stuff in Yellowstone.  And, because Plan A did happen, money got spent elsewhere, time got compressed, objectives changed on the road, and such, I once again rolled into Yellowstone once again with nothing longer than a 70-200.  And I'm not sure I even took a single photo of any animals on that trip into the park, choosing instead to just do some nighttime wide angle stuff for a night, and move on down into Grant Teton.  Now, I have to say that part of the reason I only spent one day in Yellowstone was because I managed to get the one shot I had in my mind on the 2500 mile drive out there.  Had that not happened, I probably would have spent a few more days in the park seeing if I could do any better this time with the 70-200 than I had in the three or four other times.  Maybe.

So, I can't say how a 200-500 would have worked in Yellowstone.

But, last spring I had a new-to-me 80-400 with me in the Alps, and it was an indispensable lens.  I often just had it as my walking-around-town lens, and loved it.  Too heavy for me to take up into the mountains, but in town, my climbing partner looked at my photos, compared to his, and said it was like we weren't even on the same trip.   I seriously doubt I would have taken a 200-500 to Europe, even if I had one.  My bags were already so jammed and heavy, I was almost thinking of leaving the 80-400 behind, but I'm so glad I didn't.

Driving all the way out there?  There's no way I wouldn't bring these two lenses:
24-120 f/4 and an 80-400 f/4-5.6

I just wanted to mention the 24-70.
I used to travel with it (24-70 L) but found it was neither wide enough nor long enough to do everything I wanted without resorting to "foot zooming"
It is a great lens, but better for wedding venues than outdoor shooting

We did the Grand Canyon, Antelope Canyons and a bunch of other stuff around those areas.  
I brought a 16-35 & rented a 100-400  
The 100-400 was overkill.  Didn't need that much for what we did and saw.

If you have a 70-200, Id rent a 16-35 f/2.8 and call it a day with just those two. Examples from my trip with the 16-35.  (Also, if you're going near Flagstaff, absolutely stop by the observatory, it was amazing.)

Yeah, if you can only have 1.

My Hawaii trip involved 3 lenses:

24-120
70-300
11-16

and a travel tripod.

Sure, I would have liked to have the 200-500, but with those three lenses I was able to capture pretty much any scene I wanted.

You can cheat a bit for landscape panos (i.e. drop the 11-16) with multiple overlapping shots and stitching them together in post, but there's no way to cheat long lenses in post work unless you like pixelization (though I must say I was pleasantly suprised at LR's upscaling function the one time I've used it).

I use the Tenba cases, fit well in backpacks and provide excellent protection.

It's all fun and games until you're on the beach at sunset taking "sink below the horizon" shots and a whale decides it's time to try to fly.

Sunset 20170221 Humpback Breach by FredMan, on Flickr

Sunset 20170221 Humpback Breach by FredMan, on Flickr

Sunset 20170221 Humpback Breach by FredMan, on Flickr

Sunset 20170221 Humpback Breach by FredMan, on Flickr

And these are cropped all to hell and back.

I appreciate all of the above, but the last time I was "out west" what I didn't have was a lens w-i-d-e enough. 24 is wide but if it was me I'd think of having something less along. A lot of prime lenses are pretty small and light so less of a deal to stash an extra lens or two.

ETA
Or something like the 16-35 mentioned above.

I have a D750, live in Ohio, been to the Grand Canyon (many times).

24 -120 F4 N

Hey, I love my 14-24 f/2.8, but OP doesn't even want to take 2 lenses, let alone the 3 lenses I would be taking, at a minimum.