Our standard week (but we have only been doing this half a term)
Monday: Mostly at home, maybe to the park or DD1 (5) might go out after school time to play in the street
Tuesday: Often meet up in one of the local museums with one or two other families. Dancing lessons after school
Wednesday: Either stay at home or go to a museum. Rainbows after school for DD1. After Christmas, DD2 (3) will start football after Christmas.
Thursday: HE art club in Newcastle every other week, in the opposite week we often meet up with other families, or chill out at home. After Christmas DD1 will be doing football after school.
Friday: Local shopping centre to do some shopping (as a task for the kids really, I do the main shop online) and go to the library.
At the weekend we sometimes go to visit people, go to the ILs for Sunday lunch, etc - the stuff we were doing anyway.
Plus obviously playing in the street whenever and having friends for tea, going to birthday parties and so on.
Whenever we go anywhere, DD1 asks for her bus ticket, orders in cafes etc, so that she is learning day to day interactions. There are also often special events - eg this week we have been to a cathedral to learn about christmas and we are having a HE christmas party tomorrow at a soft play centre. We also went to the "mainstream" christmas party at the community centre on Tuesday as dancing is now off for Christmas. Next week we will be going to look round a fire station with the HE kids.
We also sometimes go along to a playgroup for DD2 (although DD1 plays too, to "help the babies"...)
We do some nature walks now, but hoping to step that up a bit in summer. I know that isn't exactly "socialising" but it is out of the house.
I do get the impression that we do more than the families who have been doing HE for a while though. There is another regular meetup that we never get to because we are too busy.
I am very shy, but weirdly HE has made me make more friends, because I force myself , iyswim. DD1 is relaxing and getting much better socially too, because she isn't being overwhelmed.