Rate these areas?

[Trufflemarmite]

I have a very small budget to buy my first London property (under 300k). I know I will only get a studio or 1 bed for this. I have rented in London in Richmond and Archway. I have done some research and have narrowed possibilities down to a few areas. All very different but transport not too bad to Holborn where I work. I am looking for a lively but safe area (not too rough around the edges as I often work late). I need to be close to a station. Please mumsnetters help with views on what is best out of the following:
North Finchley
Streatham Hill
Crystal Palace
Acton/Ealing
Blackheath

I have visited all the areas and whilst they are very different there are things I like about all of them, and transport is reasonable.
would be really interested in any thoughts! Thank you.

I only really know Blackheath (and to a lesser extent Crystal Palace). I would happily live in Blackheath. You would get more for your money in Lee though, which is not too far away from it.

Thank you. What’s Lee like?

Well it's not as nice as Blackheath!! It is rougher round the edges. My experience there is not recent (had relatives living there a decade ago) but I looked on rightmove after you posted and the places in your price range (although bigger) in Lee wouldn't fit your other criteria, so you'd be better off in Blackheath tbh.

Sydenham might also be worth a look.

I am prepared to sacrifice space for a ‘nicer’ area. Just hoping that prices come down a bit! Thanks for your help. I will try and visit Lee on one of my trips and see what I think.