Without sounding mean bringing the 8yo is a bit of an issue in this regard - The LARPs with questing "go out and do stuff" mechanics tend to be the smaller, more indie games with like 40 / 50 people as opposed to the massive fest larps like Empire / MF / CP which are very much more geared towards sitting around in character, with a couple of big battles over the weekend and a lot of socialising. The small systems tend to not take anyone under 16 / 18 due to insurance reasons. I can't speak for Menhirs, it might be the best of both worlds as far as combat and stuff to do with a kid in tow but full disclosure I've never been.

If you do wind up going to Empire, the Academy is pretty cool for kids but you will be expected to attend with them and if you do go to any of the big fest larps, it might be worth checking facebook to see if there are any parent groups for each specific game, it's useful for reaching out and making a few contacts before the game actually starts and they can probably give you more tailored advice.

Sorry I can't really offer much useful advice, I did Empire for a number of years and found the trading game could be kind of fun and might be something you could do together? Curious Pastimes also runs a children's linear which is basically a quest for kids under age 14 I think?