Levada do Alecrim is a popular levada that is easy to walk. It's 6.8 km in total (out and back) with no incline.
Walking the levada is tranquil and nice, but you don't get many marvelous views. Only in the beginning. You can do the levada and waterfall in two hours if you don't do any breaks. 

The reason why we love it is for the "happy ending" being the waterfall, where you have to go for a dip. You can even jump from the top if you dare. 

Our video from this levada: https://youtu.be/jvEn60I8cd0?t=794