The walks along the levadas are flat; it's easy walking, and the views of the hillside terraces and/or the sea are great. If you aren't planning to rent via car, you can probably find a local company doing small-group tours that provides transportation from Funchal up to the levada. I don't know whether any of the levadas are accessible by public bus without an uphill walk. If you want to do this, inquire locally about appropriate levada walks if you have an issue with heights. I think some of the levadas might have segments bothersome for some folks. I think you'll find at least one levada-walk guidebook available, and it might provide all the into you need to make a choice.
The island is highly scenic. Just hopping on a public bus to one of the island towns will probably yield lovely views. I remember liking the ride to Curral das Freiras. That area can be foggy, so it would be worth trying to get a weather forecast so you can choose a sunny day.