From organization to building good habits, cleaning teaches important life skills.
Throw a bunch of toys into a box.
This doesn't apply to the current favorite toys, but rather a lot of the other ones. Put the box into some out-of-the-way storage spot (closet, garage, attic). If she asks for a toy from that box, try telling her to play with something else and assure her that you haven't tossed the toy out. In a couple of months, break out the box. It will be like Christmas all over again! Fill the box with a new set of toys and repeat. In each stage of the process, try to identify toys that are no longer played with and try to get her to agree giving them to a specific friend or relative. It's much easier to get her to part with something if she thinks it has a good purpose elsewhere and won't go to waste.
If all else fails, you can always free up your time by booking weekly or bi-weekly services from a reputable cleaning company in your area. White Glove Elite serves many NYC parents who don't regret investing the money in order to have more time to spend with their children.