Hi J., I also have a 3 yr old who is interested in sports. We just joined the YMCA in Norfolk and I am really impressed with the activities. Currently, they have "itty bitty basketball"--for ages 3-5. They also have "itty bitty soccer" and swim classes for all ages (at 3 they can go without a parent in the pool...)
I know the Y can be a little expensive, but I suggest you at least call them and talk to them about their programs.
I also have my boys enrolled in gymnastics at Tidewater Gymnastics Academy. It is great for motor development, coordination and flexibility not to mention following directions. Which will transfer to other sports later on.
Hope this helps,
C.