Closing cost fees may vary slightly from lender to lender but they all have to be paid by either you, the seller, or the lender. Lets keep it simple and keep the seller out of this. So now its either you pay it or the lender pays or both.
For a slightly higher rate, the lender would be glad to pay all of your closing costs. For a lower rate you coul dend up paying for all the fees.. But for a rate in between, the lender could give you a "credit for interest rate chosen" that you can use to pay some of your closing costs. The amount varies based on the current days pricing. So find out if they offer these pricing options, pick one and lock them in.