As a former resident of Cumberland, I used the "Pawtucket" topo quadrangle from the USGS. Cost about $2 back then.
It covered most of the NE corner of RI, and included the Diamond Hill area, (good hike up the hill and great views from the top), and some of the parks in MA adjacent to the RI border.
I recommend that you check out the Cumberland Monastery Land Preservation Site, (the area surrounding the town library). Lots of good hiking in the area, (watch out for the cliffs overlooking the quarry to the west!).
You can hike in Lincoln Woods State Park in Lincoln, RI. Not much of a challenge, but nice for the kids, etc. Also good for fishing and swimming. The NW section of the park has a lot of glacier-created, rock outcrops that are sometimes used to practice mountaineering, but no mountains.
The Pawtucket topo section also covers a good part of the Blackstone River Bikeway which offers hiking, as well as biking.
https://blackstoneheritagecorridor.o...river-bikeway/
For western RI, look for maps that cover Pulaski Park & the Walkabout Trail.
RI's North-South Trail, runs up the western border of the state.
http://outdoors.htmlplanet.com/nst/nst_map00.htm
The trail runs from the beach to the Massachusetts line where it connects with the Midstate Trail, which then goes up to the New Hampshire line and connects with the Wapack trail. Probably about a 150 mile walk, in total.
https://www.alltrails.com/trail/us/r...out-trail-loop
For southern RI, look for maps that cover the Burlingame State Park & Yawgoo areas. Loads of trails in the area.
As previous posters have said, you can print free maps from the site cited. If you get a roll of clear Contact paper, (sold with shelf paper), you can do a reasonable job of laminating your maps and save some $$$.