They will love you. Have no fear!
I know lots of people who have moved to London and its a very 'happening' place. Its so diverse that you can pretty much get a bit of everything so depends what you're after!!
As for weekends, you can get anywhere in the UK in a few hrs, so stick a pin in a map and go from there!!!! You need to visit some northern cities. Manchester, Liverpool etc. I'm a huge fan of Liverpool and not just because I lived there lol. Its just a cool place. Its a very small city, just tons of character!!!! And really getting better every year. Was quite desolate when I first went in 2000!! Has had a transformation, lots of culture, big on music and fashion and creativity!
Bristol is another city I think you will really love, and not too far from London really. I stop over in Bristol fairly frequently and even as a solo female I've had no problem on an evening going out for food and sitting in a bar before going back to my hotel. Its another place full of cool surprises, lots to see, explore, eat. The market is cool!
You have all the quintessential English towns to visit. Anywhere with s cathedral or castle is usually good for a visit in my eyes. York is great! You need to go just for the street names! Whipmawhopmagate being one of the most fun! Its an old Viking settlement too, so lots of history. Chester is also nice, but I find too busy.
Then you have rural towns/villages and you are spoilt for choice. The countryside is lovely. Cornwall and Devon are gorgeous. Derbyshire. Yorkshire moors and dales. The lake district. I'd visit Kendal in the lakes
I'm actually quite taken with Shropshire where I work, bit of a hidden gem.
Scotland isn't far!! Edinburgh is only a few hrs on train, or you can even fly. A must see I think, plus you can go to loch Ness
Of course there is Wales!!! South Wales has Cardiff another great city, and amazing coastline if you visit Pembrokeshire. Mid Wales is where I live, and again its very pretty (you're welcome to stay here too, we used to be a b&b lol). North Wales is more famous with Snowdon!
And lastly you have to visit a seaside town! Go on the pier, get fish & chips, play in the arcades! Not sure about down south but Brighton is popular!
So much to see & do if you wanted to.
Wales prob should be number 1 though
Eta, don't forget Ireland is just a ferry crossing away too!!! I've done Dublin in a day!! You can fly over and fly back in one day.
Then there's the RIDICULOUSLY cheap flights to the rest of Europe....... Seriously, you can do them in a weekend too. And don't forget if you're working for a UK company you will likely get a lot more holiday time than in the US. Plus bank holidays. Average is 25 days plus bank holidays. So much play time