Wow. A light, humorous thread suddenly took an ugly turn. Ever had a sense of humor? What happened?
Fuck it would suck to be married. Do what you want bro.
+1000 
I say just sell her on the fact that it’s a great trip and that it’s something you really want to do. And make it a trip that both of you will enjoy.
One of the things that makes Boston such a great race is that the entire city celebrates the Marathon that whole weekend. There’s lots to do. Does your wife run at all? The BAA 5k is Saturday of race weekend. My wife and kids ran it, had a great time. They got to have me cheering them on Saturday, then they saw me race on Monday. We also did the Freedom Trail guided tour and a bunch of other things.
I suggest planning out an itinerary of things to do that your wife would enjoy, then present that to her so you are making it a trip for the both of you and not just for you.
Consider telling her that this has been one of your biggest goals and once in your lifetime chance, and that if you by chance get in (you will of course) that you feel like you have to do it, you would regret not doing it forever. Register, get accepted. Then you come back saying how its amazing you got in and you are so excited and then you say that while you could just fly there and do the event solo (read:cheap), it would be such a great opportunity for her to join you and make more of a vacation out of it.
This way you make the fact that you are going to do it is almost a foregone conclusion and she is focused only on the point of whether or not she wants to take a vacation…ultimately she will due to FOMO and not wanting to sit at home while you are doing something awesome, and you sound great cuz you wanted to include her on this journey.
If she doesn’t bite on joining you or brings up the cost then you just tell her this is what you want to spend your money on and that you are going, end of story. Go, live your life, enjoy the accomplishment. And congrats on the achievement btw.
The ugly turn was you suggesting he try and scare his wife into going along with his race plans with the suggestion that an affair might be the alternative.
Didn’t seem humorous to me the way you wrote it. Maybe you’re the one who needs to work on their sense of humour?