As others have mentioned here, it sounds like the one you were told about is the RIRRC landfill in Johnston.

But check out other neighboring towns with municipal transfer stations, which may (or may not) be easier or cheaper for you. In NK (just because it's what I know, not that it will be your best option), you can drop off construction debris for $200/ton with a $10 minimum. I don't think there is a residency requirement for bulk drop off, or if there is it definitely isn't enforced.