We live on 5 1/4 acres in North Kingstown. I am 22 minutes from the Gano Street exit in Providence, so depending on where in East Providence you could be another 5 to 10 minutes on the road--depending on time of drive.
We have every concievable able creature on our property from fox, woodchucks, deer, coyotes, turkeys, swans, geese, hawks, eagles, peacocks (they live next door), large mouth bass, catfish, etc. etc. etc. Western Cranston or western East Greenwich would also be rural, as well as areas of Lincoln (wouldn't be my choice, as I like being a mile from the ocean). Check the zoning---for example: on my street we can have horses, yet we are 5 mnutes from downtown East Greenwich. Also, your budget will probably be the deciding factor-----as we have plenty of rural!