The American hostages will finally come home this Sunday to meet their families. They are expected to spend two private days with their loved ones here at the U.S. Military Academy before traveling to Washington Tuesday for a public ceremony at Andrews Air Force Base and a meeting with President Reagan at the White House.

While the selection of West Point as the point of reunion has not been confirmed by government officials, there were signs everywhere here that this would be the site. Costly and frenetic preparations went on all day and into the night. Six telephone crews were out in front of the academy's stately Hotel Thayer busily installing telephones; floodlights glared in the hotel lobby, and reporters invaded in force this bleak, fortress-like complex high over the Hudson River.

Other possible sites for the private reunion were reported to be McGuire Air Force Base in New Jersey and Dover Air Force Base in Delaware. Press officers at both bases, however, said no preparations were being made for the former hostages.

The State Department has taken over the six-story Hotel Thayer, forcing all guests to vacate their rooms by 1 p.m. on Saturday, and reserving until noon on Tuesday all 170 of the hotel's small, spartan rooms, according to the hotel's assistant manager.

There were also reports here today that a press conference was being planned for 2 p.m. Monday at which the ever-growing gaggle of journalists would be able to interview hostages and their families.

"We have moved ahead on our planning, but we have not heard anything definite yet," said West Point spokesman Maj. Timothy Carnahan. "The decision will be made by the secretary of state."

Despite the planning, Army officials nervously demurred from confirming reports that the former hostages would land Sunday afternoon about 30 miles away at Stewart Air Base in Newburgh, N.Y., where they would be reunited with their families and then be driven to West Point.

At the State Department today, spokesman William Dyess refused to say when Secretary Alexander Haig would release information on the ex-hostages' reunion with their families.

When the group arrives in Washington Tuesday, Dyess said there will be a "ceremonial reception" at Andrews Air Force Base with military bands and colors guards from all branches of the service. The White House reception will follow.

According to informed sources, the freed Americans and their families will be staying in the Washington area at the Crystal City Marriott Hotel, where they're expected to take over the entire 340-room establishment. Sources said the security preparations at the hotel in Arlington are expected to be extremely tight, with security checks being made this weekend on all 300 employes. Some of the employes are Iranian, sources said.

Anticipating the former hostages' arrival at the Crystal City Marriott, the Charles E. Smith Building and Management Company has ordered 52 "very elaborate" baskets of champagne, fruit and chocolates to be distributed at the motel.

Larimer's Market of Crystal City is preparing to deliver baskets containing a bottle of Perrier Jouet Flower Bottle champagne (about $55 a bottle), a jar of macadamia nuts, a box of Godiva chocolates, French goose-liver pate, fresh Mexican strawberries and assorted other fruits. The baskets cost about $125 each.

The District of Columbia said today it remains uncertain about any possible parade or celebration in Washington to mark the former hostages' arrival. "With the emotional problems that the hostages may have, there is no way for anyone to predict what they might want, said Alan Grip, director of communications for the District. "To plan for a parade would seem a little inappropriate."

D.C. Mayor Marion Barry sent hand-delivered messages today to Haig and Algerian Ambassador Redha Malek, offering the city's help in any last-minute celebration. The District has prepared a proclamation for a day to "honor the return of the 52 Americans" that will be made official when the city finds out for sure when the hostages are coming. b

In New York City, meanwhile, where officials have been lobbying the State Department to obtain a designation as "official host city" for the former hostages and to get federal aid in planning a traditional ticker-tape parade, there was no confirmation that the freed hostages would show up.

"We have gone ahead and made all our plans for the parade, but we haven't heard anything yet from the State Department," said a spokesman for the New York City Council.

Here at West Point, guests at the Hotel Thayer say they'd be happy to vacate their rooms for the former hostages and their families, if they come. In the hotel lobby this afternoon, Army cadets were preparing to present welcome notes to each hostage and to request autographs.

The rooms where the former hostages will be staying are described as "small and spartan" by hotel manager Steve Adams. A typical room here has no curtains, and is furnished with a worn utility rug, a double bed without a headboard and a color television.