Guess they're getting a better rate than the Double Tree (what was the hotel of choice when I went through). The training center in NJ isn't really around much of a happening place...we were hold up in Freehold. Not many hotel options, but its a 45 min train ride to Philly or NYC. It could be worse. Be glad you got a job and are being put up with S&Q. You'll be in NEO with a bunch of other brand new Academy 3rds and will have no trouble finding ways to get in trouble.
You'll be in Norfolk for a week or so and the NJ another 6-8 weeks.Unless their is a huge urgency for Mates, you'll have to go through it all. Getting paid to sit hungover through power points and shoot some guns isn't as bad as it seems. Engineers might get plucked out early to go to a ship.
Once you get done with training, you'll be sent to the East Coast pool. Unless things have changed since I left, all new mates are sent East Coast. If the West coast needs you, you maaaaay get called and sent to a West Coast (Pacific fleet) ship. Once you are on your new ship...you can put in for a West Coast transfer via your detailer. I didn't have a problem getting a transfer....but be careful for what you wish for...pros and cons for both.
You'll be sitting in the pool for probably a week or two before getting called out.