| Most Londoners socialize in their own neighborhood and rarely cross the river -- pick your area carefully because it becomes your whole world.
This just flat out isn't true and is a bit of a historic trope
| Council tax varies wildly by borough, so two flats at the same rent can cost hundreds different per year in total.
Council tax is defined by the value of the property, not by the rent
| The Overground and Elizabeth Line have completely changed which neighborhoods are convenient -- don't just look at Tube maps.
The tube maps show the Overground and Elizabeth Lines as well as all the other TFL managed services. A better map of where is "convenient" is this https://neilgarratt.com/campaigns/improving-travel-times/
Having said that I 100% agree with the rest:
| Sunday in London is genuinely excellent with markets, roasts in pubs, and park life -- it's the city's secret best day.
| Cycling has become a serious commuting option with protected lanes expanding every year, especially south of the river.