Blockshopper.com and privacy issues

Those are public records. Blockshopper is pulling the data from NYC's system, as can anyone else who's interested.

Which is why many people purchase with LLCs.

What are the advantages and disadvantages from a tax point of view? What are the additional costs? thanks

Don't know, but you do have to plan ahead, so talk with your lawyer about it. If your objective is to cover your tracks (not the only reason to do it,) then you have to be punctilious about every one of the publicly-filed documents attached to the transaction. I've seen LLCs and other entities only with condos and land, so maybe co-ops have problems with them, though they're certainly OK with trusts. It may not be worth the bother, especially since the curious tend to be persistent in digging stuff up. It's a challenge.