Hi Joe. What do you wish to do in the Cinque Terre? I love the area, but I also love to hike there. I'm not sure I'd bother going there unless you really want to hike. I have not been there in March. I'm guessing it's much less crowded at that time of year, but if it's rainy, hiking might be challenging.
There are lots of lovely towns in the Italian Riviera. Portofino is really nice, but so are nearby Rapallo, Santa Margherita Ligure, and Camogli. Those three are easy to get to by train. You can walk (not much of a hike really) or take the bus from Santa Margherita Ligure to Portofino. I'm not sure if the boats connecting them will be running in March.
You could stay in one of the Cinque Terre towns or another riviera town and train to the others (but not Portofino directly).