Royal Watch: Princess Margaret proved again yesterday that she really is interested in art. She is said to be the one member of the British royal family who really understands and loves it. On Monday she paid a visit to the popular "Treasure Houses of Britain" exhibition at the National Gallery of Art. Yesterday morning she returned to the gallery to visit the blockbuster "Impressionists" show in the West Building.

The 55-year-old younger sister of Queen Elizabeth II was met by gallery Director J. Carter Brown and then shown through the exhibit by Brown and senior curator Charles Stuckey. She was with a small entourage of companions who didn't disrupt the normal flow of visitors to the exhibition. And she was not disturbed by people who were there to see the show.

Later in the day she visited the Phillips Collection, where she toured Washington's little gem of a gallery with Director Laughlin Phillips, his wife Jennifer and curator Willem deLooper. As at the National, the visit went on without incident. One visitor to the Phillips, who had been at the "Treasure Houses" exhibit, laughed and said, "Oh, no, is she here today?"

When you have a royal for lunch, there are rules. Now, the British royals are famous for their affection for animals. But when the princess agreed to have lunch at the Phillipses' Georgetown home it was suggested that the family's dogs and cats not be present. They were sent to the vet's for the afternoon. Also suggested was Robertson's Barley Water and Royal Grouse whiskey. The princess had the water but not the whiskey. Gorbachev Versus Cosby at Stanford

Stanford University students have invited Soviet leader Mikhail Gorbachev to be their June commencement speaker, but if he doesn't accept, the second choice is television star Bill Cosby.

Even though White House officials have said no firm date has been set for a Gorbachev summit meeting with President Reagan here in June, students at Stanford contend the June 15 speech could tie in with the meeting. Seven Stanford seniors, in a letter published Monday in the Stanford Daily, objected to Gorbachev's speaking because they "can't think of anything more boring." One of the Stanford senior class presidents said Cosby is a viable alternative because he is "someone who is reflective of feelings many of the class members have." Whatever that means. End Notes

Singer Yoko Ono, best known as the widow of slain Beatle John Lennon, will be in Washington April 7 for a one-night performance at the Warner Theatre. She will be here as part of a world tour, which includes 14 dates in Europe beginning at the end of this month and two in Canada. The 52-year-old singer will appear at Radio City Music Hall in New York on April 10. Other U.S. tour dates are still being scheduled . . .

The Washington Heart Association is hosting a Valentine's Day benefit Feb. 14 at the Old Post Office Pavilion. The celebrity star of the event is scheduled to be Donna Ashlock, the 14-year-old California girl who received a new heart from her classmate and friend Felipe Garza . . .

Undaunted by the warmer weather, the Shoreham Hotel has constructed a 36-foot, 50-ton ice sculpture of the Statue of Liberty in front of the building to kick off an "I Love New York" celebration. New York Rep. Mario Biaggi was there for the unveiling of the statue yesterday, which in this weather may not last too long . . .

It took a little longer than usual, but National Museum of American Art Director Charles Eldredge got the proper clearance for a photograph of the newly acquired Thomas Eakins painting to be reproduced in the museum's March calendar, which circulates throughout the world. And there turned out to be no problem with showing the fairly graphic nude descending a staircase. The painting was purchased at the end of last year for $500,000 and was given to the museum by R. Crosby Kemper Jr. of Kansas City, Mo. It is considered one of the last major Eakins works to have been in private hands. Titled "William Rush's Model," it will go on display March 1 . . .