We live overseas. Have a house we rent out but in a bit of a remote area. Over the next couple of years, two of my kids will be going to uni in the UK. We want to sell our house and to buy a 1 or 2 bed flat/house in the London area where we have friends and family (all over, from North London through to Surrey). We have about 400k max and we want an area with excellent transport connections. We don't know yet where the DC will go to uni but we want them to have a base where they can leave their things, go at weekends and for us to have a base in the UK too (we have a younger child who would come with us too during holidays). We had always stayed with family during holidays but now that's not possible as the family member downsized and moved into sheltered accommodation so we also need somehwere to stay when we come.
While the flat is empty, we would consider Airbnb (aware that it's limited in London) or some other short term rental. Potentially only for one of the bedrooms if we do a 2 bed.
So my question is - what areas of London would you recommend for the money we have? As I mentioned, top priority is excellent public transport links. Then ability to generate some income (as we're losing the rental money).