I don't think I've ever stayed at the same place twice in my trips to London. I've never stayed near Islington either. Usually, I'm in the Kensington/Bayswater/Paddington areas. The best place I stayed was the Royal Horseguards near Embankment but they must have been running a deal through Travelocity the time we stayed there. We looked into going back there this year but the room rate was something like 300 quid a night. There should be lots of useful info in the "Going to See the Arsenal, Want to?" thread.
There isn't anything right next to the stadium, but there are some hotels nearby. The Jury's Inn Islington is nice and is about 100 GBP per night. It is near the Angel station. I also stayed at a B&B the Europa Hotel near the Tufnel Park station. It is small and plain, but at 30 quid per night for single and breakfast it was good on the pocketbook. I also walked to the stadium, about 30 to 40 minutes.
I almost always stay around Kings Cross. It's been cleaned up a lot and will continue to be because of Eurostar moving to St Pancras. 3 stops to Arsenal 4 to Liecester sq and a staright 1 hr ride to Heathrow. Every thing there from 0 to 4 stars (5 soon) and if you want you can nip over to Brussels on the Eurostar for a pint or 5
Here's an article that might help: Washington Post: London Hotel Options, From Budget to Deluxe Of course for my upcoming trip I read the article, ignored it, and used Priceline. There are message boards where the more thorough (read: anal) Priceline users swap tips on getting the best hotel rates. Here's one: Better Bidding I took the advice of one person who had this whole bid strategy laid out and did pretty well, getting the Hilton Olympia for around US$80/night. Cheers.
We got the Hilton Kensington through Priceline last November. I would certainly recommend giving Priceline a try.