London is one of the safest cities in the world. Admittedly there are a few areas where I might be reluctant to venture onto unfamiliar streets at night, but they're nowhere near to tourist sights or the main hotel districts (or indeed, to the Emirates Stadium).
London has also got (despite the moans of some Londoners!) an excellent public transport system, meaning that the traveller could stay almost anywhere in London and have little difficulty in getting to Arsenal's ground (or to the central tourist attractions).
However the nearest tube station (unsurprisingly called 'Arsenal') is on the Piccadilly Line, just three minute walk away. So it would seem sensible to look for accommodation with easy access to that line. Kings Cross/St Pancras tube station is only 3 stops southwards. It's also excellently located for getting (via the Piccadilly & Circle Lines) to many tourist attractions. Given that the area around Kings Cross probably has more cheap hotels than anywhere else in London, it would seem an obvious place to stay.
As well as hundreds of small (and sometimes seedy) hotels, most of the big chains can offer accommodation in the area, including Premier Inn
http://www.tripadviso...s-London_England.html
and Comfort Inn:
http://www.tripadviso...s-London_England.html
Chris