Though the best instrument for stargazing is your own two eyes, there's nothing like bringing lunar craters, star clusters, or nebulae into focus with a quality pair of binoculars or a small starter telescope.
Around $250 will buy a refractor scope with a 60 to 90 millimeter lense (about two and half to three inches), a tripod mount and a couple of eyepieces. Look for one with a filter , not for solar viewing, which should never be done directly, but for observing the Moon. Seen unfiltered, the glare of the full Moon can be as painful as a car's headlights. Also, steer clear of the generic models sold at discount department store chains.
A pair of 7x50 binoculars offers a comparable field of view and magnification of an entry-level telescope for a bit less money. Planetary conjunctions, lunar occultations, even the next great comet, will look just as sharp through good binoculars. The view suffers only with the lack of a tripod mount. You may want to brace yourself against a tree for steady observing. On the otherhand, binoculars are much more portable than a telescope, a handy feature if you have to drive beyond the glare of city lights to do your stargazing.