I have finished the Silver Dragon quest and returned her eggs. She then teleported me to what I thought was the exit out. I killed everything within this area, but found only one exit that lead me back to the underdark cavarns? How do I get out of here?

Look at your map - there are two exits. One RIGHT where she teleports u (that leads to the exit above ground) and the one at the bottom u fight to get to (leads back to underdark).