Honestly, while it may not be illegal, if you walk into a police station & tell them you're going to be conducting a gun transaction in their parking lot, they'll probably ask you if you were dropped on your head as a small child. I really wouldn't advise this method of doing business.
No, private gun sales aren't illegal, but you're better off keeping the transaction on the DL & drawing as little attention to yourselves as possible. If you're leary enough of a transaction that you think you should do it at the police station just to be safe, you should probably find another buyer/seller you're more comfortable with. I wouldn't hesitate to keep on driving past a buyer/seller if the situation didn't look right. Get down the road a bit and call them to let them know what's up & then decide if the deal is salvageable.