This city, hailed recently by the Wall Street Journal as the "star of the Snow Belt," is a paradigm of the Reagan age. A private- public partnership is converting its downtown into a model of upscale attractiveness and healthy enterprise. But behind the glamour of its fresh facade, a fiscal starvation diet is rotting its muscles and bones.

From the 25th floor office of Mayor William H. Hudnut III, you can look down on the lunchtime crowds in the plaza of the restored City Market, over the roof of the Market Square sports arena, past the new riverfront park and several close-in townhouse developments, to the domed stadium rising beside the convention center and the luxury hotel, to the expanding Indiana-Purdue University campus, with its complex of state-of-the-art medical and sports facilities.

For anyone who remembers this city in the '60s as sleepy and seedy "Naptown," the new Indianapolis is a revelation. Thousands of visitors to last month's National Sports Festival made the same discovery.

But in a talk on the city's financial picture shortly after the festival closed, Hudnut pointed out some gaps in the picture of progress: in 1977, the city resurfaced 213 miles of roads; in 1979, 138 miles; in 1981, 15 miles. Of its approximately 470 bridges, 19 need replacement, 30 need major repair and 64 are usable only with severe weight restrictions. Since federal fund cutbacks began, 10 community centers have been closed and 140 supervised programs ended. A sinking fund for capital investments has been exhausted. And while the number of city employees has been cut 27 percent in the past decade, the unfunded liabilities for employee pensions in this decade total at least $86 million.

The source of the squeeze is three-fold. Like most older cities, it suffers from suburbanization. In the 1970s, merged Indianapolis-Marion County lost 28,000 people, while surrounding counties gained 83,000. Hudnut says that "every day, 125,000 people commute into Indianapolis to work, but they contribute nothing in taxes for the services they use."

They contribute nothing because the Indiana legislature has tied the city's fiscal hands, forcing it to rely essentially on the local property tax. In 1973, the legislature rolled property- tax rates back 20 percent and then froze them. As a result, Indianapolis' revenues have not come close to keeping pace with inflation in recent years.

The third step has been the cutback in federal grants-in-aid, which -- even though Indianapolis has never been a "tin-cup city," in Hudnut's phrase -- provided 25 percent of the city budget.

Hudnut, like Sen. Richard G. Lugar (R-Ind.) before him, has earned a reputation as one of the Republicans' leading spokesmen on urban affairs. As chairman of the National League of Cities, Hudnut says, "I supported new federalism in 1981, but you reach a point where you have to say enough is enough. When you see two-thirds of the cuts coming out of the 14 percent of the budget that includes our grants-in-aid, and nothing coming out of defense or entitlements, then you decide that maybe they are out to get you."

The mayor's complaint does not negate the evidence that this city is doing many important and exciting things for itself. The private sector, led by the Lilly Endowment, is putting millions, not just into traditional charities, but into long-term investments like the sports and recreation facilities.

As James T. Morris, vice president of the endowment, says, the trustees have put about $50 million in downtown projects -- half of it for the domed stadium -- in the belief that for cities like Indianapolis to survive with no inherent advantages of climate or location, "we have to have an environment that gives people an extra degree of confidence. There has to be something here that makes the people with skills and with capital say, 'Yeah, I'd like to live there.'"

Despite criticism from some center-city blacks that the highly visible projects provide few permanent jobs, most here clearly believe it is a sensible long- term strategy to identify Indianapolis as a sports-health-medicine center.

But neither foundations, nor industries nor universities are going to pave the streets or repair the bridges. That is the job of government.

And Mayor Hudnut, no bleeding- heart liberal, says, "New federalism is a fine thing, but where I live, at the end of the pipeline, it gets pretty tough. It does not deal with the fiscal disparities between cities and suburbs or the insensitivity of state government or the burden of higher taxes at the local level. . . . And some day it's going to come back to haunt us. When the infrastructure deteriorates to the point of collapse or an underclass of unemployed begins to protest, we may recognize the price of our neglect."