You have a few good options here:
Just behind Diani Beach is the Shimba Hills National Park which offers a hilly, wildlife filled break from the beach. This is really only a day trip from Diani.
Near Amboseli is the delightful, green and rolling Chyulu Hills.
But my pick would be Loita Hills and forests just to the east of the Masai Mara, a very little known and frankly wonderful place where you can do easy day and overnight hikes and enjoy a different check list of wildlife and birds.
Note though that very few safari companies know about Loita and it’s not a place you can just make your way to independently.