Cats are curious and playful animals, and there are many fun activities you can do with them to keep them entertained and engaged. Here are some ideas:

1. Play with toys: Cats love playing with toys, especially ones that are interactive. Some popular toys include feather wands, laser pointers, and small balls. You can move the toys around and let your cat chase them, or even hide treats inside them for your cat to find.
2. Provide scratching posts: Scratching is a natural behavior for cats, and providing them with a designated scratching post can help prevent damage to your furniture. You can encourage your cat to use the scratching post by sprinkling it with catnip or attaching a toy to it.
3. Build an obstacle course: Cats love to climb and explore, so building an obstacle course for them can be a fun and challenging activity. You can use boxes, tunnels, and other household items to create a maze for your cat to navigate.
4. Offer treats: Cats love treats, and giving them a special snack can be a great way to bond with them. You can also use treats as a reward for good behavior or for training your cat to do tricks.
5. Teach your cat tricks: Cats are intelligent animals, and they can be trained to do a variety of tricks. You can teach your cat to sit, come when called, or even play fetch.
6. Provide a window seat: Cats love to watch the world go by, and providing them with a comfortable window seat can be a great way to keep them entertained. You can also set up a bird feeder outside the window to give your cat something to watch.
7. Give them attention: Cats crave attention from their owners, and spending time with them can be a fun and rewarding activity. You can pet your cat, talk to them, or even just sit quietly with them.

Overall, there are many fun activities you can do with your cat to keep them entertained and engaged. By providing them with toys, treats, and attention, you can help ensure that your cat is happy and healthy.