It's a wonderful area for families. We (me, DH, and DDs 5 and 2) live in Windmill Hill in BS3 (also relocated from London a couple of years ago) and even though we've been in and out of lockdown for half our time here we've completely fallen in love with it. The community spirit, particularly in the last 12 months, we've found amazing and completely different to the anonymity of (in our experience) London neighbourhoods. And yes, the farm is brilliant, as is Victoria Park, but the great thing about Bedminster is that if you get bored of what's on your doorstep it's only a 15 minute walk to Wapping Wharf and the harbourside (where there are restaurants and galleries and museums, and in non-covid times festivals, boat trips, even steam trains). The 'shopping' centre of Bristol is a bit further but still only a 25 minute walk. We were initially looking at Southville but came further east because of house prices and are so glad we did - all the shops and cafes of North St are still really close, but we're much better connected (a 15/20 min walk to Temple Meads, or it's a single stop from the local station) and you get much more from your money. Don't know Knowle anywhere near as well, but there are lovely parks and nature reserves there, too; from what I understand housing stock seems to be more 1930s semis (with commensurately more outside space) than the Victorian terraces we have down the hill. (The one downside for us has been not having a big garden, but that's more than made up for by the benefits of being so close to everything.)
Note that there are various developments on the cards around here - high-rise student accommodation, mostly - but they've been knocking around for a while and keep being quashed by local residents' groups. One or two do seem to be moving forward now, but having been adapted to make them much more beneficial to the local community - sadly, there are parts of Bedminster that are quite neglected and these developments, though by no means perfect, should go some way towards improving things. East Street at the moment has a lot of vacant shops but they're trying to encourage new local businesses in. There's no doubt the area is gentrifying, which is of course worrying in some ways, but there are a lot of people making a tremendous effort to ensure improvements happen in a way that benefits the whole community rather than just the up-from-Londoners clamouring for artisan bakeries and microbreweries (both of which we do also have!). The main reason I mention all this is because a) if you do end up buying round here, particularly up the hill, it's worth checking how the potential developments will impact you - the view west towards Ashton Court will in particular be changing, and b) in my completely inexpert opinion, if you're bothered about return on investment, I think purchasing around here will turn out to have been a very smart move in several years' time.
Anyway - I could rave about Windmill Hill and Bedminster for hours, but do PM me if you've any specific questions. Bristol as a whole is an amazing city - we have no family or background here but are so very glad we moved - and there are lots of lovely areas, but even if we had a bigger budget I honestly can't think of any part of the city that would be preferable to where we are now.