re the activities, I live in a big city with a large HE community. I would say that there wouldn't necessarily be activities organised. It really, really depends. And what I would be aware of is that these are not necessarily going to be drop off activities at this age-in case you were hoping to squezze some work in (honestly, I wish!). Eg swimming, IME, is not an organised thing round here but a group of us meeting up.
To be perfectly honest I've organised plenty of stuff in the past and have kind of got to a stage with it where I can't be bothered. I just do stuff with my own kids really. I love my many HE friends-I go to groups, and meet people socially all the time-, but in terms of organising stuff, I've got a bit fed up with people not showing up, having to either arrange for everyone to pay me or worry that people will not show up on the day and so I'll be out of pocket, etc. Because I have three kids, its often not worth it for me to go as a group-its often not far off the same price for me to, say, get a tutor in, or possibly split it with one other family (HE families are often large). Not trying to put you off but I'd get in touch with your local group (facebook is how many meet nowadays) and really get a feel of how much is being organised.
Also, some groups are highly structured, very "top down" and/or work with the LEA, others are more parent-led and loosely structured, basically a group of parents chatting around a table. Its worth trying a few groups, if you have the option, to see what works for you 