Bexley Village is an okay place to live. I left there three years ago. Some things to note: it gets absolutely rammed with drinkers in summer. It can be very, very loud. Try to avoid buying on the high street because of this.
Second thing is, the crime rate has doubled since I left, and I've no idea why. In national average terms, it's still very low (<150 per month), but worthy of a mention.
Third thing: they're digging underneath and around this area here:
https://www.google.com/maps/place/51%C2%B026'18.9%22N+0%C2%B009'19.9%22E/@51.4389835,0.1538652,17.34z/data=!4m13!1m8!3m7!1s0x47d8ae708f5a8e0f:0x6e1140de9692d39c!2sHuntington+Cl,+Bexley!3b1!8m2!3d51.4383269!4d0.1533602!16s%2Fg%2F1tqt8ydx!3m3!8m2!3d51.4385833!4d0.1555278?entry=ttu
to upgrade the power lines. The one in that field is called the Hurst site. I think they might've built a sub station there, I can't quite recall. I know the reverberation of them drilling with machines the size of lorries overnight kept the other half awake (they're not meant to, but when they're behind schedule, they just do it anyway and email the surrounding residents a little bit in advance).
When we left, there were going to be 150 lorries a day going through that field; they built a road through the middle of it specifically for it. The project was going to last six years.
You need to look into what it's done to traffic in the area, because there aren't many roads, they're narrow, and it's a tiny village, and it's just off the A2 which gets MAJOR rush hour traffic, plus people detouring via Bexley whenever there's an accident, which is pretty common, especially towards Blackfen, a little bit further down the A2. It's possible that it's living hell getting through there these days, but you need to speak to someone with some up to date local knowledge to confirm or deny.
https://www.nationalgrid.com/national-grids-london-power-tunnels-breakthrough-completes-ps1-billion-projects-tunnelling-activity
Honestly though, if I had a budget as good as yours, I'd chose Blackheath instead without a moment's hesitation. Yeah, parts of it are 'naice' BUT, there's far, far more to do, and you can choose between so many places to eat and drink that you can and almost will find places with more laid back people.
I mostly found the locals think the Village is 'naice' anyway, so if you're looking for a location to live where that sort of mentality isn't too rife, you need to look elsewhere. They don't live in Bexley or Bexley Village, it's 'The Village.'
The really big added advantage with Blackheath is that you have very easy access to Greenwich and all the wonders it provides, of which there are many.
Of the other places you mentioned, you missed Hither Green, which is just up the road from Lee (which has nothing notable). I really liked it when I lived there years ago, and although there wasn't a lot going on (20 + years ago), it was extremely easy to hop on a bus to Blackheath and Greenwich and access all that goes on there without having it on your doorstop. Some stunning Victorian conversion flats there <3
Plus Hither Green has two different train lines into London; so you may still stand a chance of getting in on time if there's a problem on one of them.