I don't post so much anymore, but I'm a Tottenham fan.
Funnily enough, growing up in North London, my first ever match I attended was an Arsenal FA Cup match (against Ipswich Town if I remember correctly). Despite being only about six years old, I quickly realized that Arsenal fans are generally a bunch of bell-ends
so I soon started to support Spurs and have been suffering ever since. However, this has improved over the last five or so years.
I also learned that Spurs are the original team from North London with the goons being the impostors who moved north of the river from South London many years ago.
All joking aside, I do agree with what some others have said, should you down the road decide to go and watch a match, trying to get to some crappy backwater like Stoke will prove challenging.
So that being said, it might be wise to pick a team in or around London. Of course, Manchester or Liverpool are also doable, but not generally as simple as getting to London. Liverpool is harder than Manchester because you would have to fly to London or Manchester and then get to Liverpool from there (not that far from Manchester mind you).
Spurs are often a lot of fun to watch. We've got a good history but haven't won much recently. We are just finishing building a nice, state of the art stadium too. Despite not having revenue coming in that Man U, Man City, Chelsea, Liverpool, or Arsenal do, in the last few years we have quite well and I would say that only Man City really had our number. Then again, with the money they have....very few teams can compete.
If you want to pick a London team that is not in this top tier, you could go for Palace (good atmosphere) or Fulham (nice family club). You'll likely find it easier to get tickets to those matches than the clubs I mentioned. I wouldn't pick West Ham, purely because their stadium probably has even less soul than the Arsenal one. Watford are quite far out in NW London.
COYS!