Both the "J" and the "I" are Vivaldi ... with some modification.
Jameson Inn is ... are you ready for this ... Stone Serif and Stone Serif Italic with the slant removed from the J and the I ... and the "AMESON" and "NN" superscripted. I didn't check it but it could just be Stone Serif Italic completely with the slant removed. The text has also be condensed.