It sounds like you need increased strength and endurance in the leg muscles including, but not limited to, the quadriceps (front of thigh), hamstrings (back of thigh), and all leg and hip muscles. In addition, you want to work on balance after having surgery.
I would recommend that you find a physical therapist to work with in order to assess and determine what exercises would be most beneficial for your particular situation. You can look under Find a PT at www.moveforwardpt.com
Definitely do follow up with this since the strength is extremely important with the functioning of the knee.