Pleasant Grove is an unincorporated community and census-designated place in Muskingum County, Ohio, United States. The population was 1,726 at the 2020 census. Pleasant Grove is close to the geographic center of Muskingum County and is at the southern end of Washington Township. It is bordered to the south by Wayne Township and to the …Pleasant Grove is an unincorporated community and census-designated place in Muskingum County, Ohio, United States. The population was 1,726 at the 2020 census. Pleasant Grove is close to the geographic center of Muskingum County and is at the southern end of Washington Township. It is bordered to the south by Wayne Township and to the southwest by the city of Zanesville, the county seat.