No, Hubble cannot take photos of the Apollo landing sites.
An object on the Moon 4 meters (4.37 yards) across, viewed from HST, would be about 0.002 arcsec in size. The highest resolution instrument currently on HST is the Advanced Camera for Surveys at 0.03 arcsec. So anything we left on the Moon cannot be resolved in any HST image. It would just appear as a dot.
Here is a picture that Hubble took of the Moon:
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