HI there!
I was told by my vet that you should not take them outside to pulic areas until they have had there third set of shots. At that age they can very easily pick up any illness. If you have a yard that no other dogs ever go in then it would be fine for the pup to run around out there and burn off some energy
. But also be sure to put a sweater or coat on if it is even a little bit chilly.
Also, do you have an area to block him in during the day, like a laundry room or an x pen? (try to use baby gates instead of closed doors so they can see whats going on) This way he can run around during the day and not be all well rested for mega playtime all evening!!