Same advice as everyone else here. No idea where you are coming from, but take the subway. It gets you in and out quickly and it is PERFECTLY safe. If you are coming into grand central, just hop on the 4 train and it will have you at the stadium in 15 to 20 minutes. After the game, they line up the subways and get people out of there quickly. Don't know why you heard such bad things about the NYC subway, but it is the best deal on earth...
That area of the South Bronx is perfectly safe, especially on a game day when 50,000 people are milling about and there are a ton of cops out. One other piece of advice... They won't allow you to bring drinks in bottles into the game, but you can save a ton by bringing other food stuff in. If you take the subway, when you hop off, hang a right onto 161st street (past the McDonalds) away from the stadium. There are lots of places you can get food from. On the opposite side of the street from McDs, about half a block down is one place I always go to (sorry, no idea what the name is). For example, if you buy peanuts there, they are $1.50 or $2 or something like that. Inside the stadium, the same exact bag--same brand and all--is $5. People I go with often get sandwiches there and bring them in. Way less expensive than buying food in the stadium... I always take a short walk down there and buy some stuff--even if I am not hungry--out of principle. I remembered why last week, when we got up there late for a game and I didn't have time to stop for food outside. So we stopped at the concession stand and got a hot dog (not for me), a pretzel and two jumbo beers. It cost $25. Each of the beers was $9! By the seventh inning, when drunken fights were breaking out all around me (it was Yankees/Sox weeknight game) and the idiots were getting dragged out by security, I was seriously wondering how any of these guys--none of whom looked like Wall Street tycoons--could afford to get drunk at the Stadium.