BV,
Show off.
My best "quasi-military" trip was 250 kt low-level along the coast in a Vampire T11, followed by a close-up view of the summit of Mt. Taranaki and then using the summit as a reference for some mild aeros!
Louiscoke,
Sorry. Probably not what you wanted to hear!
However, I would recommend any trip across some water to really bring home the utility of a light aircraft.
I recommend Bembridge or Sandown on the Isle of Wight for a first foray over the water. Get your instructor to take you there, including a tour around the island.
Less than two hours, including lunch, for a trip which would take all day by car and ferry.
PS Welcome to PPRuNe and good luck with your PPL.