Unless it really doesn't suit your commute, pay more to be central. This will help you see the city + be social. It can be really difficult if you are one side of the city and your friends end up being the other side as you can have an hour travel to see people type deal.
With location, proximity to a station & what train line matters - you'll likely use the underground a bunch so consider your commute for this closely.
Take one of those bus tours. I did only after living there for years as 'that's for tourists' but its really worth it and gives a good city perspective.
Do lots of travel to Europe from London. So much is on your doorstep with cheap flights if flexible on where you go. Take advantage of this especially if kids are on the horizon.
If you dont already, learn to like beer and pubs. There's something better about British pubs and pub culture. Also it usually well priced reasonable quality meals.
Speaking of pubs, anything crowded in the city will have pickpockets so watch you phone/bag closely or it wont be there.
Its quite common to rent flats furnished, this is likely a good option for you to start. Also what I did as I had no rental history there is offer to pay 6-months up front (and requested a discount for that) to show there financial risk was reduced.
Its an awesome city - I personally enjoyed immensely. I noticed people tended to be there 6-month or 6-years - it was kind of love or hate though, with the majority loving.
Oh and go to Shakespeare's globe theatre for me will you. I walked past that place for 2 years thinking I'll line that one up sometime and never did!
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