London with a Child: Tower Bridge or Kensington for a 1-Week Stay?

Planning a London trip this August with our child for a week. Can’t decide between staying near Tower Bridge (CitizenM with the bridge view) or Kensington near the museums.

We want to see the major sights, eat good food, visit cafés, and do a bit of shopping, but also don’t want to spend thousands on hotels. Which area would you recommend for a first London trip with a kid?