This is a non-issue. Presidents frequently cause local expenditures, tough shit, he’s the President. We pay for it. End of story.
The President can absolutely work from anywhere. In fact Bush spent over 2 years bedding down in places not in Washington D.C.–and that’s just counting his domestic excursions. During his eight years in office he spent 487 days in Camp David, and 490 days at his Crawford, TX ranch.
Neither are the White House, Camp David is a government property for the President’s use, but certainly isn’t as fully equipped as the White House, particularly not for the President’s staff. But the reality is the staff can largely stay in Washington and work in the West Wing, a few handlers and comm links and such and the President is fine.
In terms of security, of course, neither compare to Trump Tower. Camp David is designed for Presidential use and is heavily secured, and rural, which makes it easy. The Crawford ranch is a private residence, but is rural and on a lot of property, which makes it very easy to secure. Remember how Cindy Sheehan spent ages camped out front protesting? The ranch is so big that she couldn’t even get line of sight on the actual residence.
Securing Trump Tower for what will likely be very frequent Presidential visits will almost certainly be a nightmare, particularly since much of its floorspace outside of the 3-story Trump family penthouse are residential units for other private citizens, business offices for the Trump Organization and other businesses, or retail floor space, and then the atrium/lobby are legally public property and open to the public.
To a degree the White House has similar issues, part of the building (a small part) are open to public tours. The big concerns with Trump Tower are that it’s not “set back” at all, it’s right in the middle of busy Manhattan streets, and it’s also a tower, in a city with major air traffic and that exposes it to potential aerial threats much moreso than the White House (which is well within the area around D.C. where planes cannot fly at all.) They have closed off air space around Trump Tower, but the bubble around it is a lot smaller than the huge one around Washington.