It's great that you're going in March! The crowds will be much more manageable at all your destinations than peak summer season.
In Venice, take a vaporetto to one of the outlying islands -- Burano was great, a quaint town pictureque in a totally different way than the crazy bustle of Venice.
Consider taking the train Venice - Rome: it's under 3.5 hours on a very fast, comfortable, and affordable train service. Less time center-to-center than flying.
In terms of your interest in "curious" things, reference Atlas Obscura, it's a great source for interesting sites in any destination.
If you like his style, there are several great audio walking tours you can download free from Rick Steves's website.