[3] The birthplace of Ulysses S. Grant is located in Point Pleasant, an unincorporated community in the southern part of the township.

Located in the southwestern part of the county along the Ohio River, it borders the following townships: Campbell County, Kentucky lies across the Ohio River to the southwest.

No municipalities are located in Monroe Township, although the unincorporated community of Point Pleasant lies in the township's south along the Ohio River.

[4] The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1.

There is also a rest stop across from the Grant Birthplace and the Bachelier Park sports complex operated by Amelia Knothole Baseball.