A first-quarter moon is quite bright and worth enjoying for its beauty alone.
Try to examine the terminator of the moon with binoculars or a low-power telescope to see partially lit craters standing out in bold relief. The terminator is the dividing line between the lit and unlit portion of the moon. Craters and mountains along the terminator cast long shadows and stand out far more when the sun is either rising or setting than when the moon is full and the sun is overhead. At full moon craters and mountains cast very shallow shadows and are much more difficult to discern.
The next couple of days the moon travels through a busy part of the sky serving as a pointer to several objects of interest.
Tonight find the moon and note its surroundings. Above and to the left (east) of the moon are the Pleiades and directly to the left (east) of the moon is Taurus the Bull with its bright star Aldebaran. Friday night the moon will be just to the right (west) of Taurus. While the bright moon dims Taurus, this area will be beautiful in binoculars.
Saturday night the moon moves on to sit just to the left (east) of Taurus. By Sunday night the moon will be halfway between Taurus and bright Jupiter in Gemini the Twins. Jupiter will be to the left of the moon and Taurus to the right of the moon. Just below the moon on Sunday night will be Orion the Hunter.
Monday night things get even better. The moon will then be just below (south) of Jupiter and just above the star Alhena in Gemini, the third-brightest star in Gemini after the “twins” Castor and Pollux.