While visiting a time period, Susan fell in love with a Human and she stayed with him--she was the first companion to leave, though she does appear in much later episodes.
Yes, in Dalek Invasion of the earth, they travel forward in time to a London that has been invaded by Daleks, Susan twists her ankle and can't follow her Grandfather, so she stays with Barbara (another companion) there they are rescued by survivors and a boy called David, she eventually falls in love with him but can't decide whether she should go with the Doctor or stay with David. The Doctor locks her out of the TARDIS deciding that she shouldn't stay just to make him happy and then he flies away. She gets married to David and walks off. We then see her again in the five doctors, where she helps Turlough when the cybermen are placing bombs outside the TARDIS then she goes off with her Grandfather. The last time we see her is in the Children in Need short Dimensions in Time where she comments that the sixth doctor can't possibly be her grandfather.
