Kimberly,
As you look at rentals, check how close they are to Tube stations (and which lines run there). Map out a few trips to see how long you would have to travel to get to areas you plan to visit. For example, I enjoy theater, so I always check the travel time to West End theaters.
I have stayed near Kings Cross St Pancras Station (which is close to where you would catch the Eurostar train to Paris), and it was convenient to lots of tourist attractions and theaters. There is a Harry Potter Shop nearby as well.
Kensington and Bayswater are also good choices.
As others have noted, plan several daily itineraries, so you don’t back-track too much. Also, have a few back-ups for free musuems/churches/free concerts for days when it rains and have some flexibility to enjoy good weather days with some time in parks/picnics or more walking.
For example, after visiting Westminster Abbey in the morning, you might grab a sandwich and enjoy a light lunch and walk in St. James Park (if the weather is nice), then you could tour the Churchchill War Rooms. I find that taking a break outside and walking helps me enjoy museums and exhibits more.
If you visit Westminster Abbey, the guided Verger’s tours are excellent. You can book the general admission tickets on line in advance, enter early, then book the Verger’s tour in person. I signed up for the earliest available.
For a break from museums, etc. you might visit a market on market days. That can be fun even if you just walk around a bit and eat lunch there. Here are a few of the better known that are closer to the major tourist areas:
Borough Market (I visited after a London Walks tour, which ended near there).
Portobello Road Market
Brick Lane Market
Old Spitalfields market
You might look at London Walks which offer interesting tours. You just show up and pay, so you don’t have to book in advance. They do offer a Harry Potter tour among other options.
Here is the link: http://www.walks.com/
In 2015, I took the Eurostar from London to Paris, then a train to Rouen where I rented a car to drive to Bayeux. After my trip, I saw that someone had suggested taking a train to Caen and renting the car there because it is easier to drive in and out of than Rouen is. I would agree that Rouen is difficult to drive in and out of. You can rent a car in Bayeux, but at the time, there were better prices and options in the larger cities. If you leave in the morning, the Eurostar to Paris, then a train to Bayeux or nearby city is convenient. Bayeux and Normandy are great to explore.
All the best,
Raymond