Dolomiti National Park, Feltre (also pictured above):
At the Dolomiti national park (the part in Feltre) there are some incredible waterfalls! There are two separate spots where to can get out of your car and explore; one spot is where the waterfalls pool and another where you can follow a little wooden path with a place that you can veer off and walk back through a little ravine. If you have trouble finding the two spots just buy a caffe and ask the barista.
For more pictures just Google "Feltre Cascata". Once in Feltre just ask at the bar for the location or follow the signs for "Cascata"
This one is a little bit secret. Follow the gps coordinates (46°15'39.2"N 12°44'17.9"E) using Google Maps and veer off the main road down a small paved road. You will park by a big rock pile. There is a tiny path just below the road/bridge you drove over to the gravel pile. Follow that path and wade through the water under the road/bridge. You should now be able to see the first waterfall. If you want you can climb up that waterfall and there is a second waterfall that pools up there.
Grotte Di Pradis:
This last one might not be technically allowed but Grotte di Pradis is open on the weekends in the summer. There is a set path they intend for you to follow but there is a place near the bottom where it dips down to the waterfall. If you are feeling adventurous you can climb in and wade upstream into the canyon a bit. Be safe and don't get in trouble!
For all of these I recommend proper swim gear and water shoes you can climb in a little bit. Remember all of these are mountain runoff so the water is quite cold; go on a hot summer day!