I highly recommend an app called Tube Map, you can use it to plan tube journeys on the fly.
I’d also order and load an Oyster card so it gets posted to you in advance to save messing about when you get there. You can also load the TFL app on your phone so that you can use it in place of an oyster.
Make sure you always, always, always swipe out after you get off the tube, not all stations have physical barriers to swipe out of so you can get caught out and see your oyster balance drained super fast because you’ll get charged to the end of the line.
If you’re at all likely to want to fall back on cabs at any point due to tired feet/closed tube stations/luggage etc then download the Uber app and get it set up in advance so you’re never ever using a black cab (expensive). I was in Islington on Friday night and Angel station was closed, really couldn’t face another 25 minute sweaty walk back to Kings Cross in 30 degree heat after already trekking up the hill on the way there. It was £3 each for me and my partner to share the Uber, not as bad as you’d think for the convenience of it.
Wear comfortable shoes, don’t take this opportunity to wear new DM’s or other tricky shoes, you will regret it.
Nice things to do in London;
Sketch - walkable from Oxford Street. Lovely food, beautiful setting.
Any of the Ottolenghi restaurants.
Loads of lovely places to eat in Brixton, and just a brilliant vibrant place to wander around.
I highly recommend The Pem restaurant in the Conrad St James, head chef Sally Abe was recently on Great British Menu. Beautiful setting and decor - Suffragette inspired, service is outstanding (Emma Underwood recently won Best Front of House in the GQ awards - and it’s totally deserved, she made us feel like old friends). Quite spendy (but probably quite reasonable relative to fine dining in general), circa £150 for three courses for two adults - no alcohol, but the short courses such as canapés bread, sorbet, etc are gratis. The Mango and passionfruit sorbet was one of the most beautiful things I’ve ever tasted in my life.