The Fairfax County Board of Supervisors opens a two-day retreat Monday to grapple informally with a host of the county’s most pressing issues, such as transportation funding, diversifying the tax base, understanding the financial criteria behind the county’s credit rating, finding a new county executive and stream­lining the elaborate planning procedures for redevelopment.

But perhaps the most urgent question will be whether Supervisor Gerald W. Hyland (D-Mount Vernon) will sneak squirrel meat into his recipe for Brunswick stew, which will be served at lunch.

The retreat, at the Workhouse Arts Center in Lorton, will be the first for the board since all 10 members won reelection in November. It also will serve as a prelude to a joint retreat planned for Feb. 25 with the county’s newly elected School Board.

There is a list of topics on the supervisors’ agenda, but there will be no formal action, and there’ s no telling where the talks will go.

The last time the board held a retreat, at Frying Pan Farm Park in July 2009, the county executive raised the idea of taking over local roads from the state, and the debate quickly turned to whether Fairfax County should declare itself a city. It was a discussion that not everyone on the board was ready, or eager, to have.

But several supervisors said they look forward to the relaxed give-and-take.

“I think it’s really useful to hear from people what their priorities are,” Supervisor Pat S. Herrity (R-Springfield) said. “We don’t often have a chance to get together and really talk when we don’t have a formal agenda.”

High on the list of topics for Chairman Sharon Bulova, who leads the board’s 7 to 3 Democratic majority, will be streamlining the county’s planning process, funding transportation, enhancing the public’s participation in county business and finding a successor for County Executive Anthony H. Griffin.

Griffin has given notice that he will step down this year after more than a decade as the county’s top manager. He is scheduled to give his perspective on governing Virginia’s most populous jurisdiction in an address Monday afternoon.

The county’s financial advisers also will discuss the criteria used by ratings agencies to analyze a government’s creditworthiness. That has been on county leaders’ minds since Moody’s Investors Service decided last year to put Fairfax County on its credit watch with a negative outlook because of U.S. budgetary problems and looming cuts to federal spending, the lifeblood of the local economy.

Bulova said land use also will be a dominant theme of the retreat. The massive redevelopment underway in Tysons Corner has presented the county with numerous opportunities but also poses challenges.

Last month, Griffin told the board that he was shifting personnel and adding two positions to the Office of Revitalization and Redevelopment to manage the work created by 15 major land-use applications and other issues raised by Tysons Corner’s transformation into an urban hub. After adding seven positions for Tysons in 2010, Griffin said he would propose hiring additional staff when he presents his fiscal 2013 budget.

With the county steadily changing from a suburb to a more urbanized edge city, county leaders want to discuss ways to revamp the planning and redevelopment process, Bulova said. Fred R. Selden, director of the Department of Planning and Zoning, will open that discussion Tuesday.

Herrity said he wants to focus on transportation funding, particularly as it relates to Tysons Corner and the $2.8 billion extension of Metrorail to Dulles International Airport.

Herrity has expressed concern that the county has failed to account adequately for transportation and other infrastructure costs in Tysons, potentially saddling taxpayers with a heavy bill. He also has raised concerns about funding the second phase of the Dulles rail project’s construction and particularly its impact on Dulles Toll Road commuters, who are helping to fund the project.

At a recent board meeting, Herrity urged Fairfax County to follow Loudoun County’s lead in pressing for a full accounting of the operating costs for the entire Silver Line extension.

Supervisor Catherine M. Hudgins (D-Hunter Mill) said she, too, looks forward to discussing transportation funding and other infrastructure needs as the date approaches for Metro to finish the first leg of the extension in Reston next year.

But she also would like to broaden discussion about how Fairfax County Public Schools and the board could coordinate their goals and services in a more holistic way for residents. It could mean social services agencies would share space with schools staff and work more closely to assist families in need.

“It’s very much a trend to ask what’s happening before school and what’s happening after,” Hudgins said. “That one’s the biggest thing on my mind.”

Members of the public are invited to attend, although seating at the Workhouse Arts Center on Ox Road is limited and there will be no forum for public comment.