You can ship your X5 by car carrier, I've done a few times but vice-versa, from NJ to SF, the cost is between 800 to $1000 and it takes about 10 days. I used Autolog.com and Dependable auto shippers, both worked out good.
You can get a place in Jersey for $2k a month no problem, try Englewood, Fort Lee if you want to be real close to Manhattan, or, if you want to save more money then you can go around 15 to 20mls into Jersey and take a train to Manhattan, you'll be there in about 30min.
BTW, it's not a lake, it's the Hudson River you have to cross and I wouldn't recommend driving in Manhattan, it's a real pain in the a$$.
Pm me if you'd like more info. I'm in the process of moving back to CA.