I think that sounds like a fine plan! Some easy rushes I've personally had experience with (that are still running, and that I recommend) include the following:
War Paint: if nothing, just watch it for the two leads, who are phenomenal, and who knows if Patti Lupone will ever do another musical in this country? I was able to get rush for this show relatively late in the day with no problem.
Bronx Tale: I've rushed this show twice. The first time, I was literally able to get a ticket less than half an hour before curtain, and it was front row center, which I loved, especially for a show like this one. The second time, I rushed it with three of my friends, and we were all able to get tickets. I think we arrived at the box office around noon for a 3:00 PM performance.
Play That Goes Wrong: I haven't seen the new cast, but the material itself is great, and the original cast did the casting for the replacements themselves, so I trust that they chose great replacements. It's a hilarious show, and I've rushed four times. Not once have I arrived right when the box office opened, and I've never had a problem getting a full view ticket.
Anastasia: You'll have to do standing room to get the cheap tickets here, but honestly, the view is great, and you only really miss like one or two things in the entire performance. For this show, you actually HAVE to show up closer to curtain because they don't start selling SRO until the show completely sells out, or at least is super close to selling out. In my experience, like 30-40 minutes before curtain is a good time to check it out.
Hope you have a fun trip! Best of luck to you in the lotteries!
