The easiest object to see in the night sky is often the Moon. The Library Telescope will give excellent views of the Moon with surprisingly different views at different phases of the Moon and can sometimes be viewed during the daytime.
The inner planets (Mercury, Venus, Mars, Jupiter and Saturn) are easily seen when visible in your night sky. Mercury is somewhat difficult to see as it is always close to the Sun. Be sure to never point the Library Telescope at the Sun as permanent eye damage may occur. Venus and Mars can be very interesting, especially when they are close to Earth. Jupiter and Saturn are stunning through the Library Telescope. Uranus and Neptune are difficult to see under the best of circumstances.
Other things to see include stars (double stars can be spectacular). Nebula and galaxies can be visible though often appear as fuzzy spots depending on seeing conditions and surrounding light.
The constellation guide provided in most kits describes many deep sky objects. Look for objects marked with an “M”, signifying one of the 110 “Messier” objects. These are easy to look up on the web and on many planetarium apps. They are often pretty bright and fascinating things observable in binoculars or small telescopes.
The LTP scope has a very wide field of view, meaning you get to see a large part of the sky. Most beginner telescopes give views rather like looking through a straw. Start your viewing using low power (set the zoom to 24). This will allow you to find things better. Use high power sparingly, as things will be bigger, but dimmer and will leave your field of view quite fast. Some targets, like the Andromeda Galaxy (M31) or the Pleiades (M45) are surprisingly big and are best seen using a low power, as this will give you a bright, wide field of view.