There's a Fairfield Inn & Suites right at the terminal. I think that's a Marriott family member.
Closest Hampton Inn is across the bridge in Fairhaven, although Hampton is Hilton
Residence Inn isn't much further away.
You can go to Google Maps and put in the ferry terminal and then click the Nearby Button and pick Hotels. That's how I found the above
Fairfield Inn and Suites is in walking distance to the ferry terminal and downtown New Bedford. Lots of really nice restaurants in the downtown area. There is a decent Hampton Inn in Fairhaven. Only 10 minutes away. You will have to pay to park in the lot at the ferry terminal if you are staying at the Hampton. Nothing outrageous but if you are using Fairfield Inn as a base, you can just leave your car there. Both are good choices. If you are staying at the Fairfield Inn, ask them for the harbor side, not the Route 18 side.
I would recommend staying at the Fairfield Inn in New Bedford. Literally walk across the street and you are at the Ferry terminal. Also, Downtown New Bedford is awesome and a great place to walk around and find some good food! (Try Whaler's Tavern)