I've gone twice now. The first time we just got in our seats and then got rained out, so we returned a year later on rain check tickets.
If you're going to be there for a few days (ie, not just going strictly for the ball game and leaving) - IMO, you want to stay in Manhattan. Our first time there, we stayed in the Bronx and all that meant was a longer subway rides to Manhattan. When we went back for our second visit, we stayed at the Park Central New York in Manhattan - and it was amazing. Much cleaner than the Bronx and we could basically walk where we wanted to go.
I'd recommend you do the stadium tour as well - but note you have to call ahead and get tickets well in advance, as it sells out.
That all said - I'd rather go to Boston (although I get the excitement for opening day). I have absolutely no plans to return to NYC anytime soon.