Mid August
We did a short hike to Timpanogos Falls (First & Second this time, I didn’t know there was another right above last time
)AND we saw a moose!!! Also could hear another one but couldn’t spot him. So awesome!! 
I did not expect to see anything like that since it is a shorter hike, so that was an awesome surprise!!! Pretty easy hike I would think most can handle it! If you try it, go a little bit further & there is another fall up above it.
More info here:
https://www.alltrails.com/trail/us/utah/timpanogos-falls
Utah County Homes, The Bennetts 