My-brother-in-law had problems for about a year. I have provided the URL for a long thread that relates to the subject. I agree tennis may be something in your future, but might be a little strenuous for at least a year.
http://www.medhelp.org/posts/Heart-Disease/Sternum-pain-after-By-pass-Surgery/show/252480
The first step is to get the OK from your cardiac surgeon and cardiologist. Once you have that you will need to build up gradually rather than jump right into a high intensity/impact activity like tennis. A cardiac rehab program might be able to guide you along the best path to build your strength and endurance.
Bone tissue generally takes 6 weeks to knit together. However, there are muscles and nerves obviously involved too and these feel sore for much longer. I remember the Cardiologist telling me I would be able to life heavy objects after three months but I really think he should experience a bypass for himself to get an idea of how much he is dreaming. My worst discomforts lasted about 4 months and total loss of discomfort didn't occur until exactly 12 months.