Pretty much in same position, DC now 12. Luckily we live in an area with lots going on. (I think had we stayed in the area we used to live I'd have been hard pushed to find anything). I've always enrolled her in something on a Saturday morning; started off with a music club then when that finished she started climbing. Then we had the afternoon free to go to a local festival (always a free one on here) or the museum, or swimming, or the park.
Sometimes things aren't advertised very well and you have to really look hard. We've found some fabulous events almost by accident. A wizarding event held at the local Uni was a highlight.
We joined National Trust and English Heritage, and took out annual membership to various places (one at a time). With a membership you can pop in an hour before closing and not feel you've wasted loads of money, plus you get to see the place at different times of year.
She started at a drama group a couple of years ago, which is frustratingly on Saturday afternoon, so now we have a mad day racing from one activity to another and it means we miss out on a lot, but then she is getting too big for a lot of the events we previously enjoyed.
Sundays I catch up with laundry and internet and she spends it wandering around demanding food and whining that she is bored
. If it's nice we have a whole day to go somewhere farther away , like the beach.
Mine is dx ADHD so I had to make the effort to do something, since she won't amuse herself at all. I did laugh at
I'd concentrate on improving her attention span so that she can entertain herself some of the day. Perhaps say that you are going to clean the kitchen ......so either she helps or can go and read book/lego/colour until you're done.
I assume this poster doesn't have experience of a child with ADHD? Good luck with that. Mine has been over to show me her dragon avatars 3 times while I've been writing this one post, and then back " for a hug" which involves lying across me so I can't do anything else. It is full-on, non stop. (Hence why we go out).