The castle itself was built right up against a lake. The lake is now allowed in to a portion of the castle that has sunk into the earth. It's an easy place for fresh water and fish, a wealth of opportunity easily available for the cats. It's very convenient, although in leaf-bare the edges of the lake freeze over, and the sunken castle becomes dangerous to traverse.
A cat who is a skilled swimmer could possibly, during warmer moons, swim down the sunken castle and see if anything valuable is there, but proper exploration would require some method to hold their breath for extended periods of time.
The nearest waterfall to the castle, it also happens to fall into an estaury. The estaury has a wealth of crustaceans and insects, and is an easy place to find ducks in new-leaf and green-leaf. While it takes time to travel to - as traversing directly along the cliffs is nearly impossible - it provides an excellent place to camp out for several days.
The river near the castle has two apparent sources. There's the smaller lake, leading into a waterfall and estuary; and then there's a river that extends far past what any cat of the area has traversed. This falls into a lake. The area is beautiful year-round, and many creatures use this area as a watering hole. It's a great place to find plentiful prey.
Cats don't tend to come to this area. For one thing, it's a difficult journey, requiring either swimming in the sea or climbing up and over and then back down sharp cliffs. For another, the area feels... wrong. There's something ominous about this place. For the most part, the castle cats don't consider this part of their territory... but sometimes, traversing out this far is necessary, especially in very harsh leaf-bares.
The beach is a little difficult to get to, and one risks sand in their fur and their paws, but during greenleaf it's a lovely place to frolic. Beautiful sea shells and other trinkets can be found here, and there's plenty of fish and crustaceans in the ocean. If you want seafood, the estuary is an easier - if longer - journey, but the beach is fairly large and one can fully escape the trees in this sandy area.
For now.
Sitting a few meters lower than most of the rest of the clifftops, the 'lower grove' isn't too impressive. However, lots of birds nest in the trees here, so it's a good place for apprentices to practice their hunting skills in newleaf and leaffall, when birds are migrating.
In a land so covered in trees, when even rock and stone suffers roots and plantlife, when things choke on all the greenery, here lies a roughly circular area completely devoid of trees. There is an uncanny, nervous feeling, like one is being watched. However, the sunlight is unbroken. Snow drifts in ways it cannot when the trees block it. A cat desperate for more light and to escape the canopy may make their way here.
Even with many cats making brief pilgrimages to the area, and many hundreds of collective hours and even days spent here, nothing bad has happened. But there's always that sensation, like something is watching you, and a faint feeling of dread...
The easiest way to and from the castle, this gentle slope is likely how two-legs traveled up and down. In fact, there used to be a road along this route; sometimes, one can find stones carved and made smooth for such a road beneath roots that trees grow around.
While climbing up and down the cliffs is, for the most part, possible for the cats, it's much easier to take this route for the vast majority of their territory, with only the beach and darklands requiring pure cliff travel.