In addition to lots and lots of tummy time it is time to start preparing your baby for brachiation (monkey bars).
In the very beginning this is what you can do: (quotes are from the book)
"Lay him down on his back on a flat surface, such as a bed, and put each of your thumbs into each of his hands. Let him get a good grip. Let him hold on for five seconds."
Do this about ten time a day for a minute each.
Gradually begin lifting him off the bed during your sessions. Watch him carefully, and lower him if he begins to slip.
"After one to two weeks of gradually lifting him higher and higher off the surface he is lying on, he will begin to be able to bear some of his own weight."
"Always lower your newborn to the bed as soon as you feel his grip loosening or see the expression on his face change from delight to concern. After a few tries, you'll be an expert at determining how long is just enogh. He is now supporting his own weight by hanging by his arms. It is the first step toward brachiation."
He also says that some babies prefer to hang from a wooden dowel instead of thumbs. If so, you could use a 3/8 or 3/4 inch dowel that is a foot and a half long.
Most importantly be very joyful and proud of your baby no matter what he does. Praise him when he hangs on and lets go. You want him to love to do this and have fun. If it's not fun he won't want to do it.
"Your goal is for your baby to hang for ten seconds from your thumbs (or dowel), taking 50% of his weight."
For babies under four months you should follow the gentler method of the vestibular program. I attached a scan of the balance program for newborns. I hope it's readable. It was just too much to type
I hope you find some way to get ahold of the book it is really better to have the whole thing in front of you and does contain so much information that it is hard to retell it all here.
To answer your question about outdoor activities, most, if not all, of the activities for a small baby can be done indoors.