If such a spacecraft would be launch before I die(just joking,I'm still young,13),I predict these maybe the mission primary objectives:
Observe's Neptune's stormy weather
Observe Neptune's 5 faint rings
Observe Neptune gravitional force and magnetic field
Shoot an anti-(-250oC) probe to observe Triton's seasons and plumes,why does Triton has those?
These are most probably the secondary objectives:
Observe Proteus,the Non-spherical Enceladus-sized moon of Neptune
Observe Nereid's highly eccentric orbit,the 3rd largest Neptunian moon
Search for new Neptunian moons