* Thousands on Long Island to get power back by end of Tuesday
* More tunnels open, more trains running
* Hardest-hit areas in New York and New Jersey still without power
By Barbara Goldberg and Edith Honan
NEW YORK, Nov 12 (Reuters) - Millions of New York City commuters, whose routines were capsized by Superstorm Sandy, kicked off the work week on Monday with a slightly smoother trip thanks to light holiday traffic, restoration of some train lines and an opening of the final tunnel shut by historic flooding.
Two weeks after the storm, tens of thousands of homes and businesses in the hardest-hit sections of New York and New Jersey remained without electricity, but most residents affected elsewhere were powered up.
On Long Island, where some 56,000 homes and businesses remained without service on Monday afternoon, the New York state-owned Long Island Power Authority said it expects to restore power to most of those able to receive it by the end of Tuesday.
LIPA said up to 17,500 customers in Nassau and Suffolk and 29,000 in the Rockaways in New York City were unable to receive power safely because severe flooding may have damaged electrical panels, wires, outlets and appliances.
Even with the lights on, some homes remained without phone, Internet and TV service due to damaged equipment and wires brought down by the deadly storm.
At least 121 people perished in the storm, which caused an estimated $50 billion in property damage and economic losses and ranks as one of the most destructive natural disasters to hit the U.S. Northeast.
New York Governor Andrew Cuomo said he plans to ask the federal government for a supplemental appropriation of $30 billion in disaster aid - on top of reimbursements expected from the Federal Emergency Management Agency for out-of-pocket emergency expenditures.
The money would pay for infrastructure costs, housing needs, costs to local governments, and small business losses, while helping with the long-term economic recovery in New York City, Long Island and other devastated parts of the state, he said.
"The damage here is much more severe than just the out-of-pocket expense," Cuomo told a news conference. "This was cataclysmic for New York, and I think it is a wise investment for the federal government to help us to build this economy back."
President Barack Obama is to visit the city's disaster areas on Thursday.
Meanwhile, New York City Mayor Michael Bloomberg joined with City Council Speaker Christine Quinn and city Comptroller John Liu to announce an emergency capital appropriation of $500 million to repair public schools and hospitals.
Bloomberg said in a news conference that while the city will seek federal reimbursements for its expenditures, it was moving ahead without any guarantees of repayment.
"Our city has never experienced a storm as destructive as Hurricane Sandy, and financing for these repairs is as necessary as it is urgent," Bloomberg said. "These school buildings and public hospitals are resources that hundreds of thousands of New Yorkers rely on every day - and we are not waiting for federal aid to begin the work of repairing and reopening them."
The City Council will vote on the package on Tuesday.
CLOSER TO NORMAL
At the start of the work week, commuter stress was eased by the opening of the Hugh Carey-Brooklyn Battery tunnel to buses only, the return of all Metro North and Long Island Railroad Lines but one and restoration of limited service on a New Jersey Transit train line into New York's Penn Station.
"I was really afraid of overcrowding today but the train was half full," said Anne O'Malley, 46, a marketer who rides NJ Transit from Maplewood, New Jersey, to New York.
Since Sandy struck two weeks ago, O'Malley has endured four hours of daily commuting - double her usual travel time - but it was closer to normal on Monday.
The railroad is concentrating on repairing all damaged trains, restoring damaged overhead wires and washed out tracks and aligning rails, said NJ Transit spokeswoman Nancy Snyder.
Two major train lines from New Jersey into New York remain suspended. Commuters were urged to use alternatives provided by NJ Transit, including free bus trips to free or low-cost ferries across the Hudson River, some docking at 39th Street, others headed for lower Manhattan.
"Things take time," Snyder said. "Much like New Jerseyans sustained personal loss, the transit system suffered too."
For the most part, a federal holiday - Veterans Day - meant a less congested commute. It was hit and miss for many, with some bus riders reporting being stuck for more than two hours outside the Lincoln Tunnel where, Snyder said, two buses collided, injuring about 20 people.
New Jersey Governor Chris Christie tweeted that gas rationing in his state would end at 6 a.m. on Tuesday, although rationing continued in New York City under a system in which cars with odd- and even-numbered license plates can fill up only on alternate days.
Bloomberg said anecdotal evidence suggests "lines are shorter" and more gas stations have reopened, but the city's restrictions on fuel purchases will remain in effect.