Caroline Kennedy, the woman who would be New York’s next senator, is sure of one thing. Among all the hopefuls seeking to succeed Senator Hillary Rodham Clinton, she said on Saturday, there is no better choice.

“I wouldn’t be here if I didn’t think I would be the best,” Ms. Kennedy said, sitting in the back room of an Upper East Side diner around the corner from her home.

After weeks of criticism that she had not opened up to the public or the press, Ms. Kennedy has embarked on a series of interviews. But in an extensive sit-down discussion Saturday morning with The New York Times, she still seemed less like a candidate than an idea of one: forceful but vague, largely undefined and seemingly determined to remain that way.

Facing a somewhat delicate task, where she is not running for office but seeking an appointment to an impending vacancy, Ms. Kennedy avoided questions about the other possible contenders, saying she did not want to criticize them. She praised Mrs. Clinton, but said it was too soon to say how she could improve on Mrs. Clinton’s performance as a senator. She said she had been personally affected by the economic crisis but sidestepped questions about her wealth, declining to say how much money she lived on each year.