I totally get you OP, and I also get a bit stir-crazy if I just stay at home despite how much I like reading etc. I need the stimulation of other people and events.
Not sure where you live, but like PP, I am in London which is helpful in terms of free/low-cost activities. There are often talks on interesting topics at universities/centres/organisations that you can go on even if you are not associated with them. They sometimes have free drinks receptions etc too after.
I have signed up to a few websites that fill seats in theatres and other events - there are lots of kids things there and you usually pay a nominal fee (few pounds)
I keep an eye on local social media stuff for school/park/community events, although these seem to be better for younger kids
There are lots of freebies around but you do have to hunt for them. DH has a subscription to the Telegraph through work, and you get a free Vue cinema ticket once a month - we take in turns going. I get a weekly free coffee from Cafe Nero through Octopus, so I go and read in a cafe for a bit once a week with my free coffee. We have a few local museums which have a free entry day on a certain day (like first Sunday of the month etc) so I always check websites for any free dates/events.
Check what benefits your workplace offers. My friend worked at her job for 2 years before she realised that her organisation had a corporate membership to the Tate, and she got 2 free tickets for every exhibition (something I benefited from too!)