Alexa Betts wanted to place her toddler son in a day-care center downtown so that she could commute with him in the mornings and take him to lunch in the afternoons.

But she couldn't find a centrally located center, so this month she is opening one herself on the corner of 16th and K streets NW -- smack in the middle of Washington's high-rent office district.

"A private center can make a go of it downtown," said Betts, who has raised $200,000 in investment capital from Small Business Administration loans and a group of Washington and Maryland doctors. "Working executive parents want day care near where they work, not out in the suburbs where they live."

Her Child's Play Inc. center is designed for 120 children between the ages of 2 and 6, said Betts, 36, who hopes to turn a profit within two years. Tuition will be $5,000 a year, competitive with other private day-care centers, she said, and she has already received 1,000 inquiries from parents.

The D.C. Department of Human Services reports that of the 325 licensed day-care centers in the District, 10 are located in the downtown area. Most of these are run either by churches outside the business district or by government agencies for their employes.

"We do not receive many inquiries about starting up centers in the downtown area," said Willie Mae Lawrence, a government child-care specialist. "Most of our centers are established outside the business district."

Betts said the idea of starting day care in the business district is not new, but she said those ideas foundered because of the almost insurmountable task of persuading a building owner to rent to a day-care facility.

She started Child's Play in January 1983 and spent more than a year searching for 7,000 square feet of centrally located office space to convert into classrooms, bathrooms and playrooms.

The reception she received at one building was fairly typical. "The developers were aghast at the thought of little children trooping through the hallways and elevators with lawyers from one of the most prestigious law firms in the country," she said.

Betts eventually rented basement office space in the 16th Street Solar building for an amount she declines to disclose. "Let's just say it is competitive," she said of the area, where real estate agents say office space rents for $20 to $26 per square foot.

Child's Play is spending thousands of dollars to build a separate entrance on 16th Street so the children will not share the building's hallways with adult tenants. The company also is footing the bill for extensive renovation work needed to convert a former computer company's office into an environment for toddlers.

Real estate agent Vernon E. Knarr, who negotiated the Child's Play lease with the Solar building's New York owners, said he believes other developers will become interested in day-care facilities if the Child's Play center is successful.

"We have combed the city looking for space and almost every developer said, 'sounds good but show me one already in existence first,' " said Knarr. "As soon as developers see that downtown workers, including their own tenants, are willing to pay for quality, conveniently located day care, then they are going to take a second look at the idea."

Knarr said day-care facilities fit almost every zoning category in the city and require no special rezoning permits in the business district.

"It is an acceptable use," he said. "It just has to be made acceptable to the developers and building owners."

Betts said she is building her dream center -- with new toys, a competent staff, computers, space and a fully staffed sick-care unit so ailing children need not be sent home. Hot lunches will be catered and, on nice days, the children will play in nearby Lafayette Park.

"Cities are wonderful and should be used by everyone," she said. "There should be a day when it's not unusual to see children during the day downtown, eating lunch with their parents in the park or simply playing."