I am a Lincoln resident, so I have a little insight. As the article mentioned, the prior owner took some money that was supposed to renovate the Cornhusker, and he used it on some struggling hotels. Not a good move.
Downtown is not really that big and everything is walkable and safe-- that doesn't mean don't be wary of your surroundings, but it's fine. The Courtyard is closer to the Haymarket, with a lot more dining options and the University of Nebraska about 2 blocks away. The Marriott is closer to the state capitol and the financial buildings in town.
It depends on your preference, but you can't go wrong either way here. The Cornhusker has a lot of convention business and some very nice meeting rooms if you are looking for that.