But be tactful about it!
You can't stop along the road to the castle, but once you are inside you can get an excellent view of squaddies practising on the firing range set up on what was once the jousting ground.
Binoculars would make it even more interesting.
Sit in the cafe, have a cup of coffee (Nescafe, I'm afraid) or tea (Turkish is available), enjoy the views and listen to the gunfire.
Wonderful from the access road (although you should be very careful where you stop, as you are passing through a military zone...and be even more careful about what you photograph).
Superb from the first and second levels.
Stunning from the third, and best of all from Prince John's Tower which is the higest point.
You'll be able to see both west and east (St Hilarion was linked with Buffavento and Kantara castles by a system of beacons).
Worth visiting for that alone.
You'll need good footwear to visit St Hilarion. It's not a place for flip-flops (thongs) or heels, or strappy sandals.
It's also not a place where children should be allowed to roam freely. Keep them close, and keep your eyes open. There are many places where a slip could lead to a nasty fall, or worse. Don't expect EU health & safety regulations here.
The first and second levels are fairly easy to access, although the path is quite steep in parts and has steps. Access to the third level is rougher, with much exposed rock. There are handrails all the way, but the exposed rock is slippery when dry and treacherous when wet (from rain or dew).
The third level is also quite overgrown, and its deep cisterns are not protected.
It's not a dangerous site, but a visit does require some forethought and caution.