1. In 8th year, after defeating Voldemort, Harry decided that maybe he should buckle down and really learn Potions. Minerva coaxes/blackmails a despondent, not-healing-well Severus to be Harry's tutor. Chaos ensues.
2. AU, based on "Roman Holiday" -- poor-little-rich-boy Harry Potter escapes his keepers for the day and is spotted by Severus Snape, who offers to be his tour guide for the day. Professions and city of your choice.
3. Instead of being hailed as heroes after the defeat of Voldemort, Harry and Severus (who survived Nagini's bite) are treated as big a threat as Voldemort. Several / all of Harry's friends get the same treatment. In deciding to fight back or leave Britain, they learn a lot about each other.