John W. Hinckly Jr., the man accused of shooting President Reagan, arrived in Washington shortly after noon last Sunday, stepping down from the 5:30 a.m. Greyhound express bus from Pittsburgh into a seedy terminal on New York Avenue NW.

That trip had taken seven hours, the last leg of a cross-country journey that began four days earlier in Los Angeles and ended at this side-door entrance to the nation's capital, where Hinckley disembarked -- a chubby, glassy-eyed drifter in need of a shave, according to those who say they saw him.

Over the next 27 hours, as best as can be reconstructed, Hinckley, 25, lunched on a cheeseburger at the terminal's restaurant, found a room in an unobtrusive downtown hotel a few blocks away and ate breakfast quietly near the window of the ground-floor coffee shop as the Monday morning rush-hour traffic moved by outside.

He watched silently but with some curiosity as the hotel maid placed fresh towels and pillow slips in his room at about 1:15 that afternoon. And just over an hour later, using a schedule published in the newspaper as a guide, Hinckley tried to gun down the president outside a hotel about a mile from his own, according to law-enforcement sources.

"He seemed like he had a chip on his shoulder against the whole world," recalled Linda Ross, a waitress at the bus terminal's Burger King restaurant, who said she served Hinckley a cheese Whopper, without onions, and an order of fried onion rings shortly after his arrival Sunday noon.

"He was real nasty about the way he ordered," she said yesterday. When she asked the man in the short beige jacket and blue jeans if he wanted to eat his food in the restaurant, she said, he replied bursquely, "I told you it's to eat here," pulled a $5 bill from his pocket and threw it on the counter.

The woman who cleaned the small room Hinckley stayed in at the Park Central Hotel -- Room 312 -- said that the man who answered simply, "What?" when she knocked on his door, in no way seemed extraordinary. "There was nothing special about him," she said yesterday.

Hinckley's journey east actually began with a flight west. On Wednesday, March 25, he abandoned his 1973 white Plymouth Volare near his parents' home in a Denver suburb and flew to Los Angeles. Law enforcement authorities there subsequently recovered the car.

He took Western Airlines Flight 45 from Denver to Salt Lake City, then changed to Western Flight 257 for the final leg of the trip to Los Angeles. He was traveling under his own name, with the flight coupon made out for "J. Hinckley," according to airline officials.

The following day, March 26, Hinckley boarded a Greyhound bus in Hollywood and then changed buses in downtown Los Angeles, pulling out of the station at 1:15 p.m. for the ride across the country.

There are two Greyhound routes eastward -- one going south through El Paso and requirinbg no change of buses, the other, northerly with a transfer in Pittsburgh. Hinckley chose the northern route, the first leg of which retraced his journey of the day before and took him across the Sierra Nevada back to Salt Lake City.

In the Utah capital, a young man boarded the bus, sat next to Hinckley and rode with him the rest of the way to Washington. The man gave a statement to federal authorities after watching the shootings on television. He is now being held in protective custody by the FBI, which has declined to release his name, law enforcement officials said.

Rocking and swaying, the bus took Hinckley over the Rockies to Cheyenne, across the plains to Chicago and to the industrial heartland of Cleveland, where he changed buses. He changed again in Pittsburgh, and rolled on to Washington.

The trip costs $117.80, one way. There is no indication, Greyhound representatives say, that there was anything unusual about the behavior of Hinckley or the young man he rode with during the three days they spent on the road.

Hinckley's bus was scheduled to pull into the Greyhound station at 12:15 p.m., a well-worn terminal situated on New York Avenue between the skeleton of steel that will eventually become the new D.C. Convention Center and a clump of bars and storefronts housing two-bit peep shows and musty striptease houses.

The bus apparently was on time. Hinckley lingered in the bus station, leaning on a pole for a while and then sitting down on a blue plastic seat, recalled a security guard at the terminal who said yesterday that he recognized the man pictured in the newspapers.

Sometime between 1 and 1:30 p.m., Hinckley walked across the terminal to the restaurant, ordered his food and ate it sitting alone in the back, Ross, the waitress remembered. He "looked like one of the D.C. street people," she said.

Sometime later that day, Hinckley checked into the Park Central Hotel at 18th and G streets NW, an 11-story brick building constructed in 1929 as an apartment house and converted into a hotel five years ago.

The Park Central -- small rooms, narrow hallways and a facade dotted with air conditioners in every window -- is moderately priced by Washington standards. Single rooms like the one Hinckley stayed in rent for between $42 and $52 a night.

Ironically, the hotel is located just across the busy intersection from the headquarters of the Secret Service at 1800 G St. NW, and only a block away from the Secret Service's Washington field office at 19th Street and Pennsylvania Avenue.

The hotel's advertisement on page 998 of the D.C. yellow pages trumpets its location as, "Just off Penna. Ave. 2 Blocks from the White House. AAA Approved. Hotel Rooms. Suites. Television. Air Conditioned."

Hotel officials have declined to say what time Hinckley checked in or to describe his movements in any other way.

An unremarkable man who blended easily into a crowd, he went unnoticed by several Australian tourists who were staying down the hall from him.

At around 8:30 Monday morning, the day of the assassination attempt, he apparently had breakfast in Kay's Sandwich Shoppe, which is in the same building as the hotel but entered only by first going outside the hotel lobby.

Kay's owner Barry Stein recalls seeing a man who met Hinckley's description eating breakfast at a crowded section of counter space near the G Street window of his restaurant. Though Stein could not remember what the man ordered, he described him as "quiet," nondistinguishable."

A maid who regularly cleans third floor rooms at the hotel said she entered the room in which Hinckley was staying about 10 a.m.

He was not in the room, she said. But a large, two-suiter suitcase was open, filled with clothes. On the night table next to the bed sat a small alarm clock. Nearby was a telephone book and a copy of TV Guide. In the bathroom, said the maid, who asked not to be identified, toiletries were spread out on the counter.

She came back to the room after her lunch break at 1:15 p.m. to bring additional towels and pillow slips, she said. This time, Hinckley was in and responded when she knocked.

As she entered the room, she said, Hinckley took up a position by the bathroom door. "He just stood there . . . and watched me," she said. He was impassive, expressionless, dressed in his light jacket, a sport shirt and casual pants. The television set was not on.

The maid said she didn't see Hinckley leave. The desk clerk on duty yesterday refused to talk to reporters. But sometime during the next 75 minutes, Hinckley made his way to the Washington Hilton Hotel and, stepping from behind a planter as the president's entourage came into view, emptied his six-sht revolver at close range, according to police.

Shortly after the shooting, FBI agents rushed to the hotel and questioned the maid. They sealed off the room and searched through what was there.

Among the things they found, sources said, were an affectionate, two-page unmailed letter addressed to actress Jodie Foster, a receipt for the purchase of a .38-caliber handgun and a newspaper clipping listng President Reagan's schedule for March 30.

Also found, the sources said, was a copy of an article from the Dec. 10 edition of The Washington Post quoting verses from some of the favorite songs written by former Beatle John Lennon, who was gunned down by a mentally troubled one-time security guard Dec. 8 outside Lennon's New York co-op apartment.