That may not be too far off, as property taxes can be very high in NY, and a large portion of the "settlement" costs are derived of your escrow account that you need to put X amount of months of property taxes & insurance into.
How much are the property taxes on the home you are buying? On a recent FHA purchase in Orange County, NY back in April, on a $395k sales price, the annual property taxes were $4,000 + the annual school taxes were $8,000. The buyer was required to put 7 months of property taxes & 6 months of school taxes - that right there was about $6,300 just for taxes into the escrow account. Insurance was pretty cheap, only $400/year, and there was only 3 months of insurance required, so another $90, but with the 1st year of insurance that totals another $490 - so the escrow account/1st year of insurance was $6,800. Property taxes often correspond with the value of the property, so if you are purchasing a $179k sales price in the same area (Middletown, NY), then from that comparison if you were closing in April they'd only have been around $3,400.
But since your property taxes will be calculated differently than on a home in Orange County, NY you should ask your loan officer for a breakdown of how many months of property/school taxes & insurance they are estimating. Those are going to be costs that would be the same no matter what lender you choose.
The attorney fee & title costs were about $1,600, additional owner's title insurance policy was about $1,750 - totaling about $3,350 for those fees. The lender's & owner's title insurance policy are based on the loan amount & purchase price but they won't be "half" of that amount for you, however yours shouldn't be quite that much (I'd estimate roughly 75% of that amount). The closing attorney can be selected by your mortgage lender or you, in NY sometimes mortgage lenders only will allow you to use an attorney off of their list of "approved attorney's". Their fee can vary a little, but most are in the same ballpark. It's good to get a few recommendations and not just go with the first closing attorney you speak to/you are referred to (especially if the seller is recommending them).
Next is the mortgage tax, which I believe in Suffolk County, NY you just have a .8% mortgage tax based on the amount you are financing. So on a $179k sales price, 3.5% down payment, that is a $172,735 loan amount, and the mortgage tax would be approximately $1,381. Recording fees can also be expensive in NY - figure another $350.
Then you have your lender fees, which obviously will vary depending on the lender. So up until the lender fees, you have an estimated cost of around $7,700 or so. If your lender fees are another ~$4k - that would explain the total settlement costs of about $12k.
I am in Orange County, CA, not NY, so do not confuse me with being a local loan officer, but I have done several purchases in NY.