(NOTE: The images below are screenshots from a program called Stellarium, available for free at www.stellarium.org. Click the image for a larger view)
This year (2013), the summer solstice and the June full moon occur within days of each other. The noon solstice sun (shown in the top image crossing the meridian of my home in western Connecticut with the effects of the atmosphere removed) will have reached its highest point in the sky in 2013. Note its position on the point of the ecliptic (drawn in red here) that is as far north of the celestial equator (drawn in blue) as can be. The June 21 sun is in the middle of the ‘winter hexagon’, just above Orion and the star Betelgeuse, and happens to be crossing the plane of the Milky Way galaxy as well. Venus and Mercury are to the left (east) of the sun, and Jupiter and Mars are just to its right, though none of that will be visible through the sun’s glare. It’s interesting to note too that the autumnal equinox is just rising due east, and the vernal equinox just setting due west at noon on the summer solstice.
The June full moon, 2 days later, is opposite the sun, occupying the position of the winter solstice at the southernmost point of the ecliptic. – it will be low in the southern sky all night, following the same path the December sun followed six months ago. And as that full moon crosses your meridian that night, the vernal equinox will be rising in the east as the autumnal equinox sets in the west. The June 23 full moon also happens to be a “perigee full moon” (meaning its slightly eccentric orbit happens to bring it closest to earth on the same day it’s full), and it happens to be the closest perigee of the calendar year, too. While these conditions will make the moon measurably (but not noticeably) bigger, a little brighter, and produce higher than usual high tides, it is nothing extraordinary. You’re likely to see all kinds of “Super Moon” posts in the social media, but keep in mind that perigee full moons occur every 14 months and that this one in particular will not get very high in the sky.