Does the Sun orbit around anything? What is at the centre of the galaxy?
The stars are not randomly distributed in the sky. When looking on large scales, we see that (most of) the stars are grouped in clusters, or in galaxies. Our sun is of no exception: it lies within our galaxy, which is known as "the milky way"; this term was coined by the ancient greeks, since the large concentration of stars produces a white glow, with similar color to milk. It can be seen when looking in a dark (and cloudless) night. The milky way galaxy is a typical spiral galaxy, and contains about 300 billion stars; our sun is one of those stars. All the stars orbit the galactic center, though due to its size, it takes quite a long time for one complete orbit; It is estimated that the sun completes one circle around the galactic center in approximately 250 million years. (The sun, by the way, is somewhere in the middle of the galaxy - not too close to its center or to its edge).
We know today that at the center of our galaxy there is a huge black hole, that weigh about 4.6 million times the mass of our sun. The properties of this black hole can be studied using its influence on stars nearby it, whose orbits can be measured accurately using modern telescopes. It is speculated that supermassive black holes - with masses that range between millions and billions to that of our sun, exist at the centre of every galaxy, though obviously these are too far away to be observed directly. Since the density of stars is large at the center of galaxies, occasionally some unlucky star falls into the central black hole, causing it to further grow (though, very slowly).
A very nice animation made of images taken by telescopes in the last 20 years of stars orbiting the black hole in the center of our galaxy can be found here: