as you can see, lotta good recommendations for mild cigars...here are two more: San Cristobal Elegancia and Ashton Classic...most have Connecticut wrappers...
you can move up the strength scale, and the flavor scale at the same time, by trying cigars with Ecuadorian Habano wrappers...these are all medium strength full flavored smokes:
AVO Heritage,
Fuente Casa Cuba and Rosado Sun Grown,
Sobremesa,
San Lotano Oval,
Drew Estate Herrera Esteli, and Las Calaveras
several Tatuaje Monsters,
Tatuaje Havana Verocu
Room 101 Hit and Run, and Master Collection 3
Camacho Ecuador,
AJ Fernandez Last Call and Enclave
Crowned Heads La Imperiosa
My Father (lancero is my fave)