CAROL: I worship [Tom Waits]. I even mildly stalked him once … Last year, I heard he was staying at this hotel so I went there everyday and sat in the lobby, drinking massive amounts of coffee, waiting for him to walk by.
I can barely speculate which hotel Tom Waits could have been staying in the previous year. The only concert he had in 2001 was one in his home town of San Francisco, and he took a trip to Copenhagen in Denmark early in the year. He attended the ASCAP Awards at the Beverly Hilton in May, which might be what Carol is referring to (if so, she was in Los Angeles at the time for some reason – where the Palladinos live, probably not coincidentally).
Like Lorelai, Carol worships Tom Waits and drinks huge amounts of coffee. Her mild stalking of Waits at a hotel is replicated later by Lorelai, who stalks Bono at his hotel in exactly the same way.