Just because you're a "spy" doesn't mean you're not in a group of plane-spotters that plan a trip to Greece. Hell, sounds like a perfect persona to assume to me.
Put yourself in the shoes of the spy. Your choices are
Plan A: be conspicuous. Run a high risk of being stopped, but have a story and hope you can bluff your way out.
Plan B: be discrete. Try to avoid being stopped, although if you are caught you are doomed.
Opting for Plan A means you have to infiltrate a plane-spotting group. Then you have to persuade the group to go to the base you're interested in. When you get there you can only take pictures consistent with being a plane spotter, or your cover story is blown. And when you are stopped (which is certain, because photography is forbidden), you have to hope that none of your friends mention your recent membership of the group, or your curious interest in this particular base. That takes a lot of time and work, the information you can gather is constrained, and the risk is substantial.
Plan B is far easier, doesn't suffer from the limitations of Plan A, and if you do a good job of hiding your camera the risk of being caught is low. And yes, I have read too many spy novels.