I was in there last summer for a dayhike after car-camping in the nearby campground. there are a couple of backcountry sites there (you have to use the designated sites). We went into the glacier gorge area as far as timberline falls. It's great terrain and I want to go back!. You'll have to choose between Glacier Gorge or Flattop Mountain (which I would also like to do) if you only have one day. If you have more than one day, you could do both. Also plan on doing the Trail Ridge Road drive -- it's awsome. I'd recommend going all the way through, but you can take the Fall River road up to the Alpine Visitor Center and then Trail Ridge back to the east side.

There's a wealth of data here:
http://www.nps.gov/romo/
be sure to check it out.

It's a beautiful chunk of real estate. You'll have a great time there.

Keep in mind that you are not the only person thinking about going there at that particular time. You will need a backcountry permit if you plan on staying overnight in the backcountry.

Also, you want to be down (well) below timberline before the regularly-scheduled thunderstorms start sometime in the afternoon.