You'll spend the day in a paddy wagon and a night in a cell.
I've done two England soccer trips with them and they've managed to get tix for some very competitive matches (Chelsea-Man U, Liverpool - Tottenham, for example) with a couple of months notice. They can craft a package for you with hotels, transport (like private car to the stadium if you'd like vs taking the Tube and walking), and tix for as many games as you might be able to see in the time that you're there. While the big EPL teams was my focus for going, some of the best times I had was going to smaller grounds and Championship teams in between the big matches. If you're there, you might as well see as much soccer as you can.
Went and saw Burnley win the league at Charlton who went down last year. One of the most surreal experiences at a sporting event seeing both sets of fans invade the pitch and demand Charlton's owner sell the club.
For Spurs, do you belong to a supporters club in America? If so they might be able to help you contact the official office. I know they helped Chicago Spurs out a ton when we went there last year. We had like 20 people come for Southampton and got to go in the dressing rooms and out on the sideline before the game.
I'm no help on tickets other than to say pick a less attractive opponent. Getting there is a pain and there is a long walk from the tube to WHL. The good news is you'll stumble across many pubs on the way. Just know that most require game tickets to get in and getting a beer is sometimes more difficult than finding the game tickets.
Is to mind the gap.
Someone feels the need to remind everyone that Arsenal has won more trophies than Spurs. It's so embarrassing for their little brothers. There's another gap, you know.
Three European Championship trophies to only one.