My suggestions are along the same lines as the previous two replies.
As Roberto mentioned, the weather may not be ideal at that time of year so touring may not be too pleasant. On rainy days, here aren't many "indoor" activities in that area to keep busy with. The towns and the scenery are the main attraction, and the ferries between the towns may not be running at that time of year. Mid-March is a bit before the "official" start of tourist season, so not all businesses may be open, but you'll likely be able to find enough hotels and restaurants open.
Two weeks in the Cinque Terre is perhaps a bit too long, so I agree with Andrew that splitting your visit between two locations might be a good plan. There are lots of possibilities in Northern Italy.... have a look at the current RS Italy guidebook for some ideas. You could spend the first week in one location and the second week in Monterosso.
For your stay in Monterosso, I would highly recommend either Hotel Villa Steno or Hotel Pasquale (assuming they're open then). One restaurant that's a favourite with many here is Cantina di Miky which is near the train station on the main street in the new town (again, assuming they're open).
Buon viaggio!