New Yorkers are used to seeing calorie counts posted on display menus at fast-food restaurants. By the end of June, travelers staying at Courtyard by Marriott, a unit of Marriott International Inc., should expect to see similar postings at the brand's roughly 160 U.S. properties that have a bistro in the lobby.

Wanting to get ahead of proposals in the new health-care legislation—which call for the posting of some form of nutritional information at eateries across the country starting next year—Courtyard decided to roll out...