First-timers would like to do this while visiting YNP and GTNP. Want something fun but not too crazy for 1/2 day. Suggestions, please!

I haven't rafted in Yellowstone or Grand Tetons. However, I did in Moab for a half day and it was a lot of fun.

You can do a search or I'm sure others will give specific opinions.

I don't think there is much white water in Grand Teton--at least when we were there in May-June. Float trips on the Snake.

When???? Generally white water rafting declines by mid July because of reduced water flow from snow melt. Float trips are not as dependent on high water so that is a possibility.

As fmpden says, it's snow melt. When we were there, and the raft/float company heard we were from NC, he said it was MUCH better (and all the time) in NC than the Tetons.
We enjoyed the float trip at dusk for the wildlife.

I went white water rafting twice in the Gardiner area, at the north end of Yellowstone.

I can't recall the name of the company but if you Google you should find it. Both times it was in early September and the rapids were Class I and II, just right for beginners -- not too crazy, but still fun.

I also don't recall white water in the Tetons.

I took a smooth water float trip, also near Yellowstone, which was very scenic and relaxing.

We just white water rafted the Snake out of Jackson at the end of July and had a blast. It is definitely lower and less gnarly, but still amazing. I get bored on the float trips. I like to paddle the raft. We saw lots of animals and had a ton of fun. It was the first time my kids went and it was just perfect for them. I have rafted the Snake in June and it can get really hairy. I always go with Barker Ewing and do the half day float trip out of Jackson. I did my first trip with them 30 years ago and have gone many times since.

So no white water in the Tetons--but yes, plenty of it South of Jackson. You start from Jackson and get bussed there and back.

We will be there the last two weeks in August. Thanks to all who responded.