Some wonderful tenors have shone the following songs:
"Standing on the Corner" (from Broadway's The Most Happy Fella)
"Being Alive" (from Company), and "Younger Than Springtime" (from South Pacific).
Kiss Me Kate would be an awesome song. It gives the best of range allowing the tenor to utilize its tessitura to blow the minds of the audience. Definitely worth a try!
One of my favorite tenor songs is from catch me if you can, "goodbye". or Take a chance on me from little women the musical. both awesome song choices.