During the last two weeks Republicans have passed twenty bills to refund the government. The Senate has either tabled them or rejected them. Only four of the nineteen addressed ObamaCare.

The first bill fully funded the government and defunded ObamaCare
The second bill fully funded the government and delayed ObamaCare
The third bill fully funded the government and delayed the indiviual mandate in ObamaCare
The bills after this funded the National Park Service, the National Institute of Health, the National Guard, the VA, WIC, Federal Employees, Head Start, and The Department of Homeland Security among others.
 
The complete listing of bills is on the Congressional website.

The House voted yesterday to fund the National Park Service as well as the National Institute of Health during the Government shutdown. The Senate will likely reject the bills.

The House also passed a bill allowing the District of Columbia to spend its own money in order to avoid what happened during the 1995 shutdown.

For more information about Congress' right to fund things one at a time, see #Shutdown Day 2.

Supposedly because of the Government shutdown the World War II Memorial was closed, barring the entrance of Veterans who had come all the way to DC to see the monument. When they reached it they found it barricaded against their entrance and Park Police guarding their way. The WWII momument is open air memorial, there was no real reason to close it off. When Republican Members of Congress learned what was happening they went and made sure the Veterans got into the memorial.  

The Republican National Committee has offered to pay to keep the Memorial open.

According to the House Committee on Natural Resources the Administration only ordered open air National Parks that are popular tourist attractions to be closed. Other open air parks have been left open to the public.