How and where can I determine the direction of a launch? I live on the South Carolina coast and sometimes see a launch and sometimes it goes Southeast.
welcome to Space Stack Exchange.
I'm going to take a guess that you mean "how can I determine the direction prior to the event?".
Go to the launch providers website and see what advance information they give as a press kit. It may well not give anything obvious, but have a look at the inclination of the target orbit.
The rest of this answer provides some ideas of how to understand the inclination:
Very roughly, if a launch goes due East, without any later dog-legs, then the orbit inclination achieved will be close, numerically, to the latitude of the launch site. For example, launching due East from Cape Canaveral would result in an inclination of about 28 degrees. Hence you can work back from the inclination to work out its direction from the pad.
Its more complicated if the launch goes North East or South East. In either case, and still assuming no dog-leg, then the achieved inclination will be higher than the latitude. This takes a diagram to explain better.
If there are headlands in the way of the trajectory it gets complicated again as the launch vehicle will need to do an early dog-leg. The later the dog-leg in the mission the more expensive it is.
For those curious, here's an example of a launch with a dog-leg .