Where will you commute to? The areas that you can easily reach from Dulwich are very different from those that you can easily reach from Kingston!
Will both of you be commuting, or only one?
Do you have a car?
I'll ask this pretending there's been no virus, because no one has a clue about what will happen to the real estate market, but what's your budget and what are you looking for? Garden flat, small terraced house, etc? Do you want to buy or to rent?
Without all these pieces of information it's basically impossible to say much.
Just beware of all the people who will try to convince you that wherever they live is best!
My two cents:
East Dulwich good for state schools, both primary and secondary, but terrible for transport.
North Dulwich - Dulwich village too expensive and transport is even worse.
Earlsfield and Southfields are better value for money but there is absolutely nothing on the high street apart from a couple of small supermarkets and cafes.
Wandsworth common: you pay a lot for proximity to the park, but there is even less on the high street, and lots of trains pass by without stopping.
Tooting better value for money but not everyone likes it.
Kingston is lovely, it has a city feel with a great high street, but, if you work in central London, your commute becomes long.
Get a railway map and see how many lines pass through a given station. What makes Balham Wimbledon Earlsfield etc great for transport links is that so many different lines pass there: not only are trains frequent, but, if one line is disrupted, you can still rely on others.