WHILE New York City Mayor Rudolph Giuliani is cracking jokes about Disney buying City Hall, it would be hard to Minnie-mize the entertainment conglomerate's purchases in the Big Apple. In a few short weeks, ''the Mouse'' has become a major player in the New York real estate industry. The Walt Disney Company's stakes range from scores of studios used by its new subsidiary, Cap Cities/ABC, to a hotel and theaters on 42nd Street. Last week, Disney started to negotiate the purchase of Radio City Music Hall, which is currently owned by a bankrupt Rockefeller Center. Mayor Giuliani says Disney is investing because it recognizes depressed real estate values that are starting to recover. ''It's a good time to buy - they are catching the market on the rebound,'' he says. The mayor is right, says William Kinn, a senior vice president at Landauer Associates, New York-based real estate consultants. ''Prices have bottomed out and the number of transactions are increasing,'' he says. From its peak in 1989 to 1990, the commercial real estate market in New York had fallen by 20 to 50 percent by the end of 1994. The vacancy rate shot up from 8.8 percent to more than 15 percent. Rents dropped. Even a mouse could tell it was time to take a bite out of the Big Apple. Of course, Donald - as in Trump, not Duck - doesn't need to be worried by Disney's real estate foray. Though Disney will now occupy about 2 million square feet of space, almost all of it is for its own use and not as rental property. Even the proposed purchase of Radio City Music Hall falls under the category of a ''Better Mousetrap,'' since it would benefit Disney, which currently uses the theater to showcase its motion pictures. Disney would buy or lease Radio City from Rockefeller Group Inc., which had been purchased by Mitsubishi Estate Company in October 1989. The prestige office towers, however, needed renovation and had difficulty attracting tenants. Now, a Chicago investor, Sam Zell, is negotiating to buy the entire center. Disney is talking to Mr. Zell and others. ''Disney's interest helped flush out other potential buyers,'' Mr. Kinn says. TOURISTS may begin to think Disney has made New York into another theme park. They will be able to buy trinkets from Pocahontas, or perhaps Mary Poppins's mountain bikes at two Disney retail outlets. The company has already found it beneficial to premier its movies in Central Park, where a hundred thousand people can watch the big screen at once. On 42nd Street, Disney won't be the actual landowner, but will be leasing space from the state Urban Development Corporation (UDC). Disney will be highly visible, however, since it is renovating the New Amsterdam Theater and is also expected to develop a $303 million hotel and entertainment complex on the street. The company has said it intends to open a new Broadway show every year. The Times Square Business Improvement District (BID), a business group that provides security and infrastructure improvements, considers Disney a real Cinderella. ''I think we can say Disney is good for real estate values and property owners,'' says Peter Kohlmann, director of marketing for the BID. City officials are also pleased Disney is a Beauty, not the kind of corporate Beast that threatens to move offices or operations to New Jersey if the company doesn't get tax breaks. In fact, Disney will become a ''serious'' taxpayer, says John Dyson, city deputy mayor for finance and development. Kinn says Disney has a history of smart real estate investments. ''In Orlando, they bought more land than they could use on a five- to 10-year plan, then they banked it and got a handsome return on their real estate investment there,'' he explains. Of course, historians may view Disney differently, since many of them got into a wrestling match with the company over its proposed $650 million theme park, which was going to be within musket range of the Manassas Civil War Battlefield in Virginia. Last September, Disney abandoned its efforts to build the park. If Disney wants to buy more real estate, this may fit with the mayor's plans. After he said that Disney was buying City Hall, he also quipped that he had a bridge for sale. Perhaps Giuliani could rename Brooklyn, the Magic Kingdom.