Virginia Gov. John N. Dalton came to Northern Virginia yesterday and heard state police, college educators and counselors for the handicapped plead urgently for increased state funds.

But the governor seemed cool to some of their requests and said building new prisons remains his top budget priority.

"We're going to have 3,300 more inmates in the next six years, and we need to spend money to build the correctional institutions for them," the Republican governor said during a brief walking tour of George Mason University in Fairfax County.

Dalton, various department heads and members of the General Assembly's Senate Finance and House Appropriations committees arrived by chartered bus from Richmond. They spent most of the day touring several facilities here in preparation for Dalton's 1980-82 budget.

During each of the governor's Northern Viriginia stops, representatives of the facilities pressed their particular program and construction needs. He listened and asked questions, as did several legislators.

"We're the only home-based state university in the most rapidly growing area of the state," argued Dr. George W. Johnson, president of George Mason University. He escorted Dalton around the campus and lobbied hard for the university's $20 million budget request for three new buildings and renovation of another.

Noting that the school's present enrollment of 11,000 is expected to increase to 16,000 in the next few years, Johnson said the university "is coming into its own as a regional resource."

But Dalton and Del. Richard M. Bagley (D-Hampton), chairman of the House Appropriations Committee, questioned plans to build more on-campus living quarters for the students, saying the school had been intended to be an urban institution without dormitories.

Johnson told them, however, that George Mason has become "an urban institution in a suburb" and was surrounded by expensive residential housing. "There's just no place to house or feed these kids unless we do some of it here," he said.

George Mason was among some 50 state facilities visited during Dalton's eight-day budget tour, which will end Thursday.

Dalton said he sympathized with the university's situation, "but we've experienced the same thing everywhere we've been. We have to determine the priorities and how to allocate the money."

Virginia's prison population will climb to 12,800 by 1985, Dalton said, but enrollment in public schools is expected to decline about 25 percent during the next 14 years.

The demand for prisons is increasing, Dalton said, which the need for school facilities "is leveling off." In answer to a reporter's question, the governor said the new prisons he wants to constuct would include training facilities for inmates.

"We're not just building these facilities to house them," he said.

Two Northern Virginians on the House Appropriation Committee, Dels. Dorothy McDiarmid (D-Fairfax) and Vincent Callahan Jr. (R-Fairfax), said the northern portion of the state has been getting favouable consideration in recent state budgets.

"It's an exaggeration that we don't get back what we put in [in taxes]," McDiarmid said.

Dalton's first stop in the Washington suburbs yesterday was at the state police station in Groveton. There, he heard Capt. Robert Suthard, chief of the 2nd division based in Culpeper, argue that Northern Virginia should be made a separate division.

Suthard said troopers assigned to the Northern Virginia area should be given higher living allowances, and he complained that population and traffic demands in such an urban setting mandated creation of a police division with its own supply and division facilities.

In addition to visiting the Groveton state police facility and the George Mason campus, Dalton's tour included the Northern Virginia Community College's Alexandre campus and the Northern virginia Training Center for the handicapped in Fairfax.