Harry is growing up with the Dursleys and nobody is very happy about this. The last straw is when some bad accident happens that could have ended with death of the whole family. Harry's accidental magic somehow saves them, but Vernon is blaming Harry from the incident and he wants to take revenge on him - and starts doing so immediately, trying to "dissolve" the threat Harry poses for his family, force him into submission and hereby "protect" his wife and son from the "dangerous little maniac." Despite her jealousy, Petunia understands that Harry didn't want anything bad to happen and that he saved them all. She dislikes Harry strongly, but doesn't wish him any direct harm, or at least not in front of her eyes. She knows she can't protect Harry from Vernon's rage, so she believes it would be the best if Harry left their house - forever, and as quickly as possible, before Vernon gets too far. She has no way to contact Dumbledore or anyone from the magical world, but then she remembers that there might be one wizard she knew some time ago. She packs Harry the few things he has, gives him some money for train and/or bus tickets and the house address, where Severus Snape lived thirteen of fifteen years ago...

With his aunt's doubtful blessing, his papers, a rucksack, a few pounds and a short letter for Snape, Harry is sent to the north of the country to find himself a new guardian. His aunt also told him never to come back and not to mention his relatives' names to anybody. If this man, the black haired Severus Snape or his father Tobias no longer live there, he should ask someone to help him and go into an orphanage. To the people around Privet Drive and to Vernon, Petunia says that some distant relative of Harry has suddenly appeared and taken him to his home (whether or not Vernon believes that is not important - in his point of view, Harry could be send to Siberia for bear hunting and he wouldn't care).

Harry is 8-10 years old (his letter hasn't arrived yet) and doesn't know anything about magic. His aunt told him that he is "strange" and that this Snape person would be the same as him. Now he has to get to Spinner's end and find him, hoping for a new family, a father; at the same time he is afraid of this mystical dark Snape figure. He has a very vague knowledge of how the man should look (Petunia hasn't seen him for at least 10 years and even then she wasn't interested in him in any way, and she didn't try that hard to describe him to Harry). He has only a small amount of food with him, the rest he should purchase for the money Petunia gave him. He still doesn't know the real value of money very well (after all, he never had any money). Can he manage to find Snape? And if he finds him, how will Snape react?

Bonus points:
1. Get Harry to Spinner's End. How can the small child not get lost in the big city and in transport? (let him travel through London. There may be big troubles waiting for him). There may be people asking for his parents or if he needs help, and people he will get into trouble with everywhere, like homeless people etc. What if he got robbed? What does he find fascinating on his trip, how long does it take to him, how would he feel if his train leave a minute before him because he was confused with the platforms? What would he do with the money when he goes to the shop for food? (It's the first time he has any money, can he remain sensible and not spend it all at once?)
2. Finally there - will Severus be in the house? What time of the year is it? Will Tobias Snape still live there? And if Harry finds the house empty, how would he feel? Will he break in so he could wait for his new father/not have to go to the orphanage? How will Snape (Severus or Tobias) react?
3. Dumbledore's reaction - will he discover that Harry is missing? Will Snape go looking for Harry?

There are many more things you can play with, depending on the direction of the story, it's length etc. Don't feel too bound with those suggestions, use your own imagination. Have fun.