Newport is a beautiful place to visit any time of year, although be prepared, it will probably still be quite cold in March.
The mansions are beautiful, but check out the web site to see what will be open during your dates, as the hours of operation are seasonal for many of the houses. The bigger ones, and most commonly visited are generally open year round, but the smaller, and in my opinion, more interesting ones may not be.
http://www.newportmansions.org/
Also, if you are interested in visiting several of the mansions, or plan to come back within the year, sometimes it is a good idea just to purchase a membership to the preservation society. It gives you entrance to all the mansions for a reasonable price for one year, and the entire amount is tax deductible.
We have stayed at several Bed an Breakfast Inns in Newport over the years, and have enjoyed them all. They can be pricey, but you can often find deals off-season. I see many deals through sites like Living Social and Groupon, so you should check those out if you are interested in staying at that sort of place. Otherwise, the Newport Marriott is very nice, although pricey. They have a good restaurant there on site as well.
There are lots of great places to eat in Newport as well. Often Innkeepers are the best sources of information on where to go.
I would HIGHLY recommend taking the time to drive over the Newport bridge into Jamestown and driving into Beavertail Park. It is one of our favorite places to go. It is free and is a beautiful location to sit and enjoy the ocean or to walk out onto the rocks. It will still be quite cold in March, but it is an absolutely gorgeous location. We like Beavertail much more than any of the Newport beaches or parks. If you do go there though, be careful hiking through any tall grass. Beavertail has many deer and ticks are abundant there...and as with any location early in the spring is when they will start coming out again. If you stay on the rocks you will be fine.
You are going at a tough time of year...great because it is off-season and rates are better, but tough because lots of the great stuff Newport has to offer, like the harbor and lighthouse tours and such won't be running yet. But, you can still find many things to do.
BTW, just as an aside, someone in one of the posts above mentioned Purgatory Chasm, which is not in the Newport area. It is in Mass., over the RI line and not near the coast. Maybe they were thinking of Beavertail??
There are also several local wineries in the area, if you are interested in visiting them and doing a wine tasting.
http://newportvineyards.com/ http://www.greenvale.com/ http://www.sakonnetwine.com/trail.cfm
Enjoy your trip.