Parking at the Jefferson Memorial
Jefferson Memorial parking is rather inconvenient. There is no parking immediately near to the Jefferson Memorial except for a couple of handicapped spaces. There is free parking at three lots in the general vicinity, but each requires a bit of a hike to get to the actual memorial itself. Lots A, B, and C are along the Potomac River about a half mile away. Except during the full bloom of the Cherry Blossom season (a few days between mid March and mid April each year), you should always be able to find a free parking spot here. Unfortunately, every other major monument, including the Lincoln Memorial, is at least a mile away from this location.
Alternative to Jefferson Memorial Parking
Why not just leave your car in a parking garage and take a tour of the monuments with Nonpartisan Pedicab? This is really the best way to see the memorials. You can see all the memorials and get back to your car in about 2-3 hours and not have to worry about Jefferson Memorial parking and the long walks to all the other memorials.
Handicap Parking at the Jefferson Memorial
There are a couple of handicapped spaces just beyond the Jefferson Memorial on Ohio Drive. Vehicles without a handicap sticker can expect a $250 ticket for parking in a handicap spot. The ranger information kiosk underneath the Jefferson Memorial offers the free use of a wheelchair upon presentation of ID. The Jefferson Memorial is set back from Ohio Drive, and it is a significant walk for handicapped people to get from the handicapped parking to the Memorial itself.
Parking at the Tidal Basin Parking Lot
One option for Jefferson Memorial parking is to park for free at the Tidal Basin parking lot. Access is off of Independence Avenue eastbound just after the Kutz Bridge. You still have a longish walk from here to the Jefferson Memorial, but this location is more central to visiting some of the museums and the Washington Monument than the Jefferson Memorial parking lots.
Parking on Ohio Drive
Another option for Jefferson Memorial parking would be to park along Ohio Drive along the Potomac west of the Inlet Bridge. This location is further from the Jefferson Memorial than the dedicated parking lots, but it is also much closer to the FDR and MLK Memorials and the Lincoln Memorial. Free parking if you are able to get a spot.
Jefferson Memorial Parking and the Cherry Blossom Festival
When the cherry blossoms are in full bloom, this is a poor choice of transportation options to get to the Tidal Basin. However, there is a parking shuttle that goes down to Haines Point, a couple of miles away. Unless you are very lucky, you will likely have to park that far away. At least you will be happy to find that all the parking is free. Or, just park downtown and take a tour of the monuments with Nonpartisan Pedicab and save yourself all the hassle.
Commercial Parking Garages
Your best bet is to park at the commercial parking garage at the Ronald Reagan Building. The address is 1300 Pennsylvania Avenue NW. Main entrance is on 14th Street between Constitution and Pennsylvania Avenues. This is a central location for the museums and the monuments. Unfortunately, you are about 1.5 miles from the Jefferson Memorial from here. They never run out of space here, and prices are pretty standard for DC. If you want to not worry about finding parking or getting a ticket, then park here. Then, just take a pedicab tour of the monuments. You can go to all the monuments in about 2-3 hours on a private pedicab tour with Nonpartisan Pedicab.
More Info on the National Mall
You can get more information about the National Mall directly from the National Park Service website.