The family (myself,wife and 3 daughters,16,14 and 9 years old) are taking our first trip out West. We have never been much farther West than St.Louis.
Which of the two would you choose? We will have around 10 days to be gone.

Been to both. Yellowstone hands down.

The only thing RMNP has is The Shining Hotel, pretty cool.

Depends on whether you want to fight crowds, or stand on the continental divide in relative peace and quiet.I vote for the backbone of the continent-RMNP.

Plan to visit some mountainous places other than national parks. There's really no need to go to a national park along with all the crowds, rules and regulations. Just find some Forest Service roads that lead up into some higher elevation areas and camp-out.
I'm sure there are some guys on here from western Montana or northwest Wyoming who could point you to some good places.

Yellowstone by far is a great place to take a family or to visit yourself if you have the chance. I can still remember my first cutthroat trout I caught in the early 60's.

Unless its a money issue, you could head straight to Yellowstone and spend 1 1/2-2 days. then a days drive south to Grand Jct Colorado to see the Colorado National Monument and scoot over to Moab Ut. (arches NP) relax a few days and catch RMNP on the way home.

If you have never been to Yellowstone, that needs to be on the top of your list. Once you have done that, consider other places.

Yellowstone - Get away from the big draws like "Old Faithful" and such and you can still find quiet places in the height of tourist season to enjoy the true nature of the west. P/M me if you would like to know more info.

RMNP!!!! Been there twice and summited Longs Peak. My wife and I put on over 100 miles of hiking trails in a week. The trails and park are extremely well maintained and the experience was unforgettable. I recommend this trip to everyone, there’s so much more than the divide and that shining hotel ( been to Estes Park twice and haven’t been to the divide or the hotel lol).

Everyone should see Yellowstone once in their life. It will be crowded but try to enjoy what God put on this earth.

Thanks for the input!
Anyone have any ideas besides the National parks?
The Utah suggestion sounds pretty cool.

As all the others stated, any of the suggested places have their attractions. As a flatlander myself, I will just say that anywhere you go will be a new experience for you. Everyone should make it to the shining mountains at least once. Gotta warn you-every time I go, a little bit of me stays there. Gets harder to come back east. My favorite , is really the 4 corners region and southern Utah, and Grand Canyon. Harrison, shoot me a PM before you go and I will help anyway that I can.
If you do get above 12 thousand feet, (RMNP), take thing slow for a bit-God didn't put much air up there.

Mt Rushmore, camp. Battle of the Little Bighorn, camp in Bighorns. Yellowstone, camp,. RMNP, Etc. Etc.

If you come to Yellowstone in the fall you will not have the big crowds or outrageous hotel prices, but you will have elk bugling, aspens turning colors, miles of stream fishing to yourself, etc. Maybe even a little fresh snow on the peaks to get your trapping blood flowing.

Or start at the top of highway 2 in other words Glacier National Park, then head toward Yellowstone, cross the Beartooth Pass . There's a lot to see, the going to the sun highway is breathtaking so it Beartooth Pass, if you are out this way the first weekend in June were hosting the Western NTA Convention in Livingston and the 2nd weekend in Sept is the MTA Convention in Lewistown, the elk are starting to bugle as enough mentioned.
Bring a coat snow happens in Montana at anytime of the year.
Allan

I"ve been to Yellowstone

and am planning on taking the family there this summer.
when I went the first time, i believe it was late June, early July - and we were able to avoid most of the crowds.
there is so much to see

Check out the black hills of South Dakota,,you might not go any farther,,,not as rugged but very pretty and lots of history

Why not drive through RMNP enroute to yellowstone. It you plan to stay in Yellowstone,you must reserve your rooms now. Can be done online. The little cabins are nice for a family.

Need 3-4 days to appreciate it all. Classes and guided tours are neat. Take binocs for everyone. Read a book on Yellowstone before you go.

If you go to Yellowstone you are going to have some amazing encounters with wildlife, even from the car. Take a good camera so you have pictures to remember it by. The elk below is an example of how close you can get to a bull elk. I took this from the roadside. I also put out several trail cameras for a couple days in Yellowstone, and got some amazing photos.

If you go up through Montana, be sure to take in the National Bison Range, it is an amazing drive-through wildlife area, it takes a couple hours to drive through it and see all the wild animals, it's huge. The photo of the bighorn is just one example I have taken there. Stunning place and hardly anyone knows about it so it's not crowded at all. When I go, I get there in the evening and drive through it, then camp nearby, then drive through it again just at daylight. The animals are out and moving and you'll see everything the west has to offer. I have no trouble even getting my wife up at 5 am she's now just as hooked as I am on the place.