On New Year's Day, when so many people are vowing to lose 10 pounds and stop biting their fingernaels, local leaders are making resolutions on a grander scale.

For the mayors, county board chairmen and county administrators in Northern Virginia, 1982 is a year in which they hope to finish road construction projects, build community centers and finance water treatment plants.

Mostly, though, they see it as a year in which they must figure out how to do more with less.

As Loudoun County Administrator Philip Bolen said before Christmas, "I would like Santa Claus to bring a computer which would help people understand that it is impossible to provide expanded services while significantly reducing taxes."

Here, then, are the New Year's resolutions from Northern Virginia leaders:

* Charles Beatley, mayor, Alexandria: "To resolve to do my best to ameliorate the harshness of the present economic climate on those Alexandria citizens who are suffering from hard times; to schedule myself to give more attention to my wife, my three grown children and my three grandchildren; and to win the election for mayor on May 4.

* Stephen Detwiler, chairman, Arlington County Board: "To map out and institute a plan to get Arlington on the road to financial self-sufficiency, thereby lessening the tax burden of the individual citizen but preserving the amenities that make Arlington a superior place to live."

* Martha Black, mayor, Dumfries: "I hope in the next year to raise more money to build a community center and to try to get more involvement by the citizens in their town government. And to have more patience in achieving these goals."

* Frederick W. Silverthorne, mayor, Fairfax City: "Hold the line on the city's real estate tax by lowering the tax rate by at least 5 cents per $100 of assessed valuation; take steps to initiate a Route 123 bypass west of Fairfax City; move forward with the approved improvements to Route 123 within the city; expedite widening Pickett Road and relocate Route 237 along this new widened road; work with the Fairfax County school system to funnel students from the county's overcrowded schools into the city's under-utilized schools; declare war on drug pushers, particularly in the areas of our schools."

As for dreams for Fairfax City, "I often dream of the completion of the Metrorail line to the proposed station between Fairfax City and Vienna in 1985-86. I hope this is not a pipe dream."

* John F. Herrity, chairman, Fairfax County Board of Supervisors: "I would like to see the Springfield Bypass issue resolved to start developing a transportation system that the county needs and the economic development program in the Route 50-Route 66 area resolved."

* Carol DeLong, mayor, Falls Church: Goals for the new year include "trying to figure out the effect of federal budget cuts and to come up with adequate resources--from whatever source --to continue to run the city as we'd like and as the citizens expect."

* Muriel Gilbertson, mayor, Haymarket: "We'd like to see the sewer system finished without any more delays, and I hope that more people become involved with their town government. We need new blood."

* Thomas D. Rust, mayor, Herndon: "To complete the funding for Phase II of the Herndon Community Center; to secure funding and construct Herndon Parkway; and to provide an even higher level of service to the citizens at less cost to them, a pretty heady goal."

* Byron Farwell, mayor, Hillsboro: "My five resolutions are: to harass the citizens as little as possible; to pass no town ordinances--there are far too many laws as it is; to prevent the health department from polluting our water; to continue to send flowers to every sick citizen in the hospital; and to discourage the establishment of any new businesses and any new houses in the town," where the last house was built in 1889.

* Philip Bolen, county administrator, Loudoun County: "My personal resolution will be to attempt to do more with less."

* Edgar Rohr, mayor, Manassas: "We just hope to be as conservative as possible and to keep the progress and prosperity going."

* Kathleen Seefeldt, chairman, Prince William County Board of Supervisors: "One of my wishes is that the General Assembly would grant more flexibility to local governments."

* T.A. "Phil" Giannopoulos, mayor, Quantico: "What we need in Quantico is a lot of money. I hope we get some federal grants to fix our sewer lines, which are in desperate shape. And I'm hoping for a little better cooperation on the council."

* Jeffrey Wolford, mayor, Round Hill: "I would like to see us come up with an acceptable alternative for a water treatment facility. It's got to be resolved once and for all, whether we're going to be able to use Sleeter's Lake (as a water supply) or not."

* Charles A. Robinson Jr., mayor, Vienna: "We have some land use problems which I hope we can resolve in 1982. We are encountering some budgetary problems, and we are hopeful we can find some economies and squeeze every tax dollar for as much as possible. Above all, I'm dedicated to the goal that everyone in town hall serves the taxpayers to the greatest extent possible."