I wouldn't worry too much about trying to avoid the whole of south or east London. London's a funny city and there are slummy and rough areas literally 2 minutes down the road from rich/posh/trendy areas, so while the south and east often have the worst reputation, this is true right throughout the entire city, in North (Tottenham, Finsbury park, Hornsey, Wood green, ect) North West/West (Harlesden, Willeseden, Neasden, Kilburn, Stone Bridge, some bits of Acton, ect) there are crime ridden areas, not just East and South. Nowadays even in seemingly quiet suburban areas there are small council estates where murders actually take place. So I don't think there's much point just trying to completely avoid south and east.
Don't let this scare you though, as if your not directly involved in the gangs or drugs the crime will rarely spill over and effect outsiders. Just have a bit of common sense and don't appear like a complete victim (i.e, trying to buy drugs off some random guy whose offering, or seeing gang of boys and obviously changing your direction out of fear) and you'll more than likely be safe in any part of London, even the rougher parts. There's plenty to see and fun to be had in east,south,north and west so don't worry too much!
Eating out in London is expensive unfortunately, but that card SC is recommending sounds good (I might have to get one!) and there's many great places to go eat. There are some good value gems of places to eat at, but it depends on what food you like. London has possibly the widest range of restaurants you could imagine! But yeah, for the best value go to any big supermaket, stock up and cook at home!
There are shops that sell second hand games, but I wouldn't bother getting your hopes up about finding Shenmue 2, it won't happen. Ebay is your best bet.
But most of all, just enjoy the city! It has so much offer, no matter what your interests are there's something for you in London. I think London is one of the best melting pots of culture, people and ideas in the world. If you have any specific interests let me know, and I'll see if I can recommend anything.
avoid cheap deep fried chicken places
What!? And miss out on the JUNIOR SPESH!!? Your trip to London would be incomplete:
[youtube]http://www.youtube.com/watch?v=Q6pbZLiLt30[/youtube]
Need I provide any more evidence of the lovelyness of our city