Opening Day seats will be super expensive everywhere especially in NYC for the Yankees. I used StubHub to buy my Yankees seats the two times I went though it was near the end of August, both against the O's. Purchased my seats for like a good 40% less then the box office.
As for suggested places to stay, if you plan on staying in the city for a bit to sightsee, then stay in Manhattan. I'm sure you can find decent hotel rates in April. If you can get a room between $200-$250/per night (taxes, fees, everything included) then thats pretty decent for staying in Manhattan. The last two times I've been to NYC I stayed at the Sheraton and the New Yorker (which is right next to MSG and Penn Station). I preferred the New Yorker a lot more, and I believe it was cheaper. Older hotel, though its right next to Penn Station and its only a couple of blocks away from Time Square. Both times I went (in 2012 and 2013) was near or on the Labour Day weekend so I think when you go in April, hotels should be fairly reasonable, especially if I paid around $250 per night close to Labour Day and with the US Open on.