With only 3 full days, you will have to prioritize. I think the 3 day London Pass might serve you well, if you are going to see a lot of sites with entrance fees it covers. We used a 3-day pass last week and crammed in so much that we saved 32.00 GBP per person!
Day 1 - after checking in and showering, go for a nice walk. Rick Steves' Westminster Walk (in his book) is a nice overview. It's important to stay outdoors as much as possible so you stay awake, therfore hitting museums is probably not the best idea this day. If need be, take a one hour nap (set an alarm) late afternoon and then get out and do something else before dinner. Maybe the London Eye on a nice evening.
Day 2 - Cabinet War Rooms in the morning (allow at least two hours, arrive at opening to beat the crowds) then after lunch, about 14:00-14:30, go to Westminster Abbey when it is less crowded. The audio guide is fabulous. You might still squeeze in another site if you are energetic. See what appeals to you.
Day 3 - Tower of London (plan 3 hours and go early!), Tower Bridge (great fun to walk across the glass walkway) and St. Paul's for a couple of hours. Rick Steves has a fun West End Walk from St. Paul's down to Trafalgar you could do after you see the great cathedral.
Day 4 - Greenwich (via City Cruise down the Thames), Windsor, the British Museum, a tour led by London Walks or something else that catches your interest.
FYI, instead of Uber, do use a black cab. There is a wonderful app called Hailo for your smartphone that you can use to hail a legal cab with all the convenience of Uber.