I visited 3 times last year for work and got to see a bunch of places.
Yes there is uber. Black cabs are expensive. And if you're using card, always ask before getting in a cab if they take the card you're using, and always have cash on you in case.
Some sites I liked:
Covent Garden. Market area with a couple pubs, shops, restaurants, street vendors with affordable items, gifts for people if you're doing that. I got a nice flat cap there for 10 pounds. Sometimes they'll have live music or street performers.
The Sky Garden - it's a bar on a rooftop that is like a big greenhouse. They have live music or DJ and it's free to go up, just pay for your drinks. It's all glass and they keep it very cool and air controlled for the plants and flowers. There's a little restaurant up there as well. you get a 360 degree view of the city, it's awesome. even if just going up briefly.
You can do a walking tour for just a few hours and hit Buckingham Palace, Westminster Abbey, The London Eye (ferris wheel by the river) and a few other sites. Hit up some pubs along the way. Pubs are absolutely everywhere. Look for ones off the beaten path.
If you like coffee, I liked Cafe Nero. Better than Starbucks.
The food there is nothing special except the fish n chips is legit good stuff. But other than that, you're better off taking advantage of cuisine from other nearby countries. They're so close to other European countries they get some really great ethnic food. For example, check out the Bavarian Beerhouse for German beer and sausages. Another good one is Barcelona Tapas - a restaurant on Lime street (near the financial district and more modern area of town) with great Spanish food and drinks.
Pro tip: difference between London Bridge and the Tower Bridge. London Bridge is just a bridge, nothing special. But people think it's the big famous looking one. The Tower Bridge is the famous one. It's right near Tower of London where the Crown Jewels are kept. It's a nice little area to walk around the Thames river (pronounced Tems). Also near the Tower Bridge is St. Katherine Pier with some shops and pubs with nice views. One is The Dickens Inn, check out the website. Been around since the 18th Century.
Another pub I sent to near the Tower Bridge area is The Hung, Drawn & Quartered. Neat history of actual site of hangings. Good "pies" (think chicken pot pies but better) and drinks.
Overall I like just walking around and seeing the little shops, stopping into pubs and getting to know the area. If you have time there are lots of great museums as well.