Buy a few annual memberships from zoos, museums, libraries

It is a good thing that you want to expose your child to activities. You can do it yourself and it will be more memorable and meaningful when you do it together.  It is not what you do, it is you are spending time together. When it is time for your child to show and tell to his classmates, your child will have fun thing to share. 

Get a few annual memberships in your local zoo, children's museum etc. With memberships, you and your child can explore leisurely and you can visit as often as you wish. You can even bring a playmate late in.

Get a cheap tent and play tent camping at a park.  
Get a fishing license, and a cheap fishing rod, and take your child fishing.

Get a simple kite.

Get a pet.

etc...