The train would take you out to Manhattan Beach in less than an hour for the price of 25 cents. Here's the route map.
According to Bob Anderson, this schedule was printed just a few years after the hotel opened. Here's what he has to say:
I think the timetable is from 1879. There are a couple of clues: Only the Third Ave. El (opened 1878) and not the Second Ave. El (1880) is shown on Manhattan Island on the map. The timetable says the line is now doubled-tracked over its entire length, which was completed after the 1878 season. And the Kings County Central branch, which ran in 1878 only, is not shown. By the way, at this time the entire MB Ry. was a narrow gauged line (3’). It was not converted to standard gauge (4’ 8.5”) until 1882.
Bob Anderson runs the Long Island Rail Road History website, where you can find just about anything you would want to know about the New York and Manhattan Beach Railway. According to Anderson, the Manhattan Beach Hotel was razed in 1907.
Sepia Saturday stop this weekend, you can see all sort of other interesting photos, some of which may relate to trains.