Mt. Vernon is open on Dec 25. http://www.mountvernon.org/calendar/view/2012-12-25/5022
You might need to rent a car to get out there.
Within the city a car is not needed to see the things you want to see.
My preferred airport to DC is Reagan National which has a Metro stop. Avoid Dulles (several reasons).
If you have any desire to see Baltimore, BWI is another great airport with good train connections to both cities.

A car is a nonsense in the city. You have to pay every time you park it - so it would actually be cheaper to take taxis that to pay for a rental car plus the garage charges a couple of times during the day as well as for the overnihgts (total parking would probably be more than your hotel).

Definitely take the Metro and walk if the weather is decent. I fyou get a really cold day (not THAT likely - hop in a cab). But do plan on walking fairly long distances between museums and/or monuments.

But - you have to make sure that you have proper clothing - or you will freeze all the time. (And snow is fairly unlikely - it typically happens that time of year only 1 out of every 5 or 6 years.)

I really think you need a rental car for Mt. Vernon on Christmas Day. It would just be so much nicer, as it's a bit off the beaten path. You will also be walking all over the estate. If it's wet outside, it would be nice to get in your car and drive back rather than wait for a bus outside. You could just rent it for a day or two.

We had free parking at our hotel, and we had three others to choose from that met our family's criteria. And you also have found a couple of properties with free parking.

I agree with NYTraveler that a car would not be helpful for the downtown or National Mall sites during business days.

We wanted to see Civil War sites, Mt. Vernon, an amusement park. So we rented a van and kept it for a week because it was cheaper than just the 3-4 days we needed it. We did end up using it for other things too, such as dinner in another neighborhood, church and parking by the Mall at night to see the monuments.

Be sure to check which car rental agencies are near your hotel. Yes, they're all at Union Station, but you'll save time if one is close by. Budget Rental Car has an outlet near Dupont Circle, as just one example.

Please check my trip report, especially Day 8, Day 12 and Day 14:


http://www.fodors.com/community/united-states/epic-east-coast-vacation-for-family-of-5.cfm

I haven't stayed in either hotel but I do know the neighborhood. The two places are a five minute walk from each other, both older buildings located on busy streets near public transportation. I might be inclined to choose the hotel with the mini kitchen and the free metro passes. There is a Trader Joe's and Whole Foods in the immediate neighborhood.

As already mentioned, you won't need a car downtown but you might want to rent one for Christmas Day if you're going to Mount Vernon. The public transport option involves the metro and a Fairfax Country bus so I would at least check what their Xmas Day schedules look like. If you do choose to rent a car, the drive down the George Washington Parkway to MV is a very pretty one. Driving in DC and environs will be a breeze.

As far as visiting Old Town Alexandria, I think things will be shut pretty tight except for the odd restaurant opened for lunch and/or dinner. Would still be a pleasant place to walk around but I'd be more inclined to visit when things are open.

I disagree about avoiding Dulles airport. While I agree Reagan National is more convenient (especially if you don't have a car), I wouldn't hesitate to fly into Dulles if the price is right.

I have eaten at the bistro in the basement of One Washington Circle and walked through the lobby. The building is older in the sense that it appears to be from the 1960's or 70's. The location excellent for the Kennedy Center (free shuttle from Foggy Bottom Metro) and obxgirl is correct about the convenience of the Whole Foods.

>>The building is older in the sense that it appears to be from the 1960's or 70's. <

Yes, I did mean older as in age and not old as in shoddy or in disrepair. One of the two hotels was originally an apartment building and that typically means extra spacious rooms but smaller baths. I'd probably opt for that esp. if it was the hotel with the kitchen.

>>that it will be very cold and about the possible lack of operating hours due to the holidays. <<

Christmas will be the only day you'll have an issue with closures at the major tourist sights and you've got a plan for that. Adding to MV and also in the city are the US Botanical Gardens (big holiday display with decorations and model trains) and all of the monuments which will be open (only the visitor centers will be closed). Just across the Memorial Bridge is Arlington Cemetery which is open Christmas Day (including Visitors Center). But MV is a good choice -- and a cab there and back might be cheaper than renting a car. I don't know how easy it is to grab one from the street on Xmas Day but you could definitely call for one.

Weather wise you can plan for upper 40s/lower 50s during the day. Could be warmer and might well be chillier.

I googled One Washington Circle and you have Enterprise, Avis and Hertz all close by. Budget Rental car is also close by (1722 M Street NW), but doesn't show up on Google.

I did a quick search with no coupon codes on Budget; Picking up an economy car Christmas Eve at 2:30 pm (they close at 3 pm), and returning it Dec. 26 at 8 am, you pay $84.90 including taxes but no extra insurance. Terms were "over age 25, 1 day 18 hour rental, unlimited free miles, 14 day maximum rental allowed."

You may want to add the insurance, and for one day it should be minimal; I don't know what your own auto policy covers but rental car companies have gotten much harsher if you do have a fender bender.

I don't know the cab rates but door-to-door mileage is 15.4 miles from One Washington Circle. Google is showing it at about 31 minutes drive, which was our experience. I wonder about getting a cab to take you back to DC, maybe a local resident can comment on that.

I agree with using a rental car for Mount Vernon; I also agree that flying ion and out of Dulles if the price is right is OK provided you realize the distance out and back and the costs of a shuttle or a more expensive taxi.