Where is the oil filter on a 2003 Honda nighthawk 250cc?

There is no "spin-on" filter, for this bike. Internally, there is a mesh screen to clean out. It just catches big particles. You don't clean it or change it regularly. You have to take one of the engine case covers off to get to it.

So, to answer your question, during oil changes you don't change an oil filter.

Don't forget to drain occasionally the crankcase vent tube. It exits at the bottom of the bike. Has a metal wire clip on a black plastic plug. Take that off using a pair of pliers. Drain the stuff out of that tube. It will fill up with time. Get an owners manual for the bike if you don't have one. You can order it on bikebandit.com, or from the dealer. It will tell you all about the oils to use, the tube to drain, and other stuff.