The 70-300mm is a very nice range for almost any outdoor sport whether it be football, soccer, baseball or motor racing. Nikon makes an 18-70mm that should work well for sports shot closer ranges, basketball, boxing, gymnastics, volleyball, track and field and so on. It would be a very useful all around lens as well. There is an even cheaper 18-55mm lens, but that leaves a gap between 55mm and 70mm which is a fairly important range for indoor sports.

The 18-70mm also gives you a somewhat larger maximum aperture at its telephoto end, which becomes important for indoor sports. This means that for indoor sports, specially with high school gyms, you will most likely have to shoot at ISO800 TO ISO1600 and accept the level of noise in order to use shutter speeds adequate to avoiding subject blur. Nikon does make a 17-55mm with a constant f-2.8 that would be a lot more comfortable for indoor sports, but it is quite costly.

There are also some third party lenses from Sigma, Tamron and Tokina in that range, and for light duty they might do fine. You get a lot of lens for your money, but often the build of the lens is a bit flimsy and quality control is not often equal to that of Nikon. They tend not to stand up well under daily use.