November 12, 2007 -- NANCY Reagan and Mayor Bloomberg have a thing going on - a mutual-admiration thing. The former First Lady is flying here for a dinner on Wednesday at Bloomberg's townhouse to raise money from about 40 well-heeled guests for the Reagan Library. "Nancy told friends recently she wants Bloomberg to run for president. She doesn't like Rudy Giuliani," said a source who recently saw Reagan in California. She and Bloomberg see eye to eye on stem-cell research, which might some day lead to a cure for Alzheimer's, the disease that debilitated Ronald Reagan in his last years. Hizzoner had lunch with Nancy last summer at the Hotel Bel Air just before he announced he was leaving the Republican Party to become an Independent. She could help him a lot in certain powerful circles in California.