They'll be within 2 degrees of each other from May 30 through June 15, and widen out to 5 degrees apart again by the end of June. An hour before sunrise on Wednesday, the waning crescent Moon is very low, just 5 degrees S of east, while bright Jupiter, just risen about 13 degrees to Moon's lower left, is just above horizon 8 degrees N of east. It's easier from S states. The Cowboy Astronomer is in its final weekend at Abrams Planetarium. This is the closest New Moon of the year.
Some coastal areas can expect extreme tides.
Hawaii time this morning, Hawaiians have a chance to see the Moon about 17 hours past New this evening. Some 20 to 25 minutes after sunset, using binoculars, try for the very slender young crescent 2 or 3 degrees above the horizon 16 degrees north of due west. North America will have to wait until Sunday evening to see the young Moon. As the sky darkens, look for earthshine on the Moon's dark side, and look for a 3rd-mag. Look again on Monday and following evenings to see how much the Moon and Venus shift nightly against the stars.