I too have a 3 year old son who is very very active. I get so tired looking after him all day while my hubby works, but he does go down for an arvo nap at 1pm, for about 2 hours, which is nice. That's when I have my 'me time'.
When we go walking, I let him walk for the first 5-10 mins, until his little legs are tired and he then goes in his 'jogger' (and I don't jog, I just walk briskly
). He loves taking a book in his pram while we walk. I can then manage to walk for at least an hour without him whinging. On the way back, we stop off at the park or oval and he has a run around and kicks the ball, before we head back home.
Another thing I was considering is buying one of those 3 wheel bikes, that also have a long handle on the back, which enable the parent to push the bike if and when the child gets tired. I thought this would be a fun alternative for him instead of going in the jogger all the time.