Smyrna School District operates schools for residents of Smyrna and surrounding areas. Smyrna Elementary School: 302-653-8588. Clayton Elementary School: 302-653-8587. North Smyrna Elementary School: 302-653-8589. Sunnyside Elementary School: 302-653-2808 John Bassett Moore Intermediate School: 302-659-6297. Clayton Intermediate School: 302-653-4512 Smyrna Middle School: 302-653-8584. Smyrna High School: 302-653-8581.