WOULD YOU GO TO PEORIA TO see people play mud volleyball? The state of Illinois thinks you might. It advertised the contest as part of its $10-million campaign to lure tourists to the state. With manufacturing in the doldrums, states are looking to tourism to generate new jobs and tax revenue.Illinois is the biggest spender in the intense competition to attract travelers.

In fiscal 1985, 10 states hiked their spending on tourism by at least 30%, led by California with a whopping 1,111%. At stake is a U.S. travel market that increased from $178 billion in 1982 to $189 billion in 1983 and still appears to be growing, thanks partly to cheaper gasoline.

It is too early to measure results, but some states are trying to extend a favorable trend. New Jersey, which increased spending from $3.5 million in 1984 to $5.5 million in 1985, has already seen the impact of tourism on job creation. In 1983, the last year for which figures are available, the state generated 16,700 jobs in travel-related businesses, compared with a loss of 14,600 manufacturing jobs. The same year, California lost 8,900 factory jobs, but it gained 6,400 in tourism.

In some cases, increased promotion is designed to hold on to a bustling tourist trade. California spent little to lure travelers until other states began siphoning off its tourists. "Suddenly, we saw these beautiful commercials with scenes of Alaska, and pretty soon those cruise ships going up to Alaska were packed," says Flo Snyder, director of California's office of tourism. To fight back, the state increased the office's budget to $5.1 million last year, from $470,000 two years ago.