The Tidal Basin is, of course, a 360-degree area. So no matter the angle of the sun, you can find a way to position yourself however you want relative to the cherry trees and the sun. Whether you want backlighting, direct sun, or shade, with a bit of walking you can find what you're after.
While that's true of the cherry blossoms, it is not, of course, true for the monuments.
You can see the Jefferson Memorial from nearly any spot on the edge of the Tidal Basin, but because of the position of the sun at this time of year, most of the most effective angles that include cherry blossoms with the Jefferson Memorial directly lit involve afternoon or setting sun. If you get there early and the sky is clear, you can get some very effective shots of the rising sun silhouetting the Jefferson Memorial.
The MLK Memorial faces southeast, which means that it catches the morning sun but is in shadow late in the afternoon.
The FDR Memorial is low to the ground and surrounded by trees, so it doesn't lend itself to early morning direct sunlight shots.
Don't Always Believe the Meter
Most cameras have a problem metering if they're pointed at the sun. There's a reason, of course--if you want a "good" photo you're not supposed to point at the sun. But sometimes that's precisely what you want to do.
The thing to remember is that the meter is only a suggestion. It's calibrated with a generic average of what a properly exposed photos is supposed to look like.
If you find that you're just ending up with a white screen or the image is far too bright, try underexposing by 2 or 3 stops from what the meter says. If you have a camera where you can set underexposure or overexposure compensation, great. If not, switch to manual and do it the old-fashioned way of just dialing down from what the meter says.
Underexposing like this has some benefits. It will often make the sun itself more defined rather than simply part of a large blob of white in the photo. It will also accentuate the natural colors. Of course, it'll also underexpose other parts of the image, so you have to make a judgement call on the look you're going after and whether you like the look of some parts being silhouetted.
All of the shots on this page with the sun in the actual frame were underexposed by at least 2 stops from what the meter recommended. The rich golden colors are a result of that deliberate underexposure in camera--they're not added in post-processing. It accentuates the natural golden light of the very early morning (or very late afternoon) sun--they call it golden hour for a reason.
Sunrise and Sunset Times at the Tidal Basin
You can find the sunrise and sunset times at the Tidal Basin here.
When the sun is high in the sky, you can't detect any movement with the naked eye. But when it's very low to the horizon, it's remarkable how quickly it is actually moving. Dawdle for too long, and you'll lose the shot. You don't want to be having to reposition too much, fiddling with your camera's settings, or changing memory cards.
In the morning, the richest colors will be with the first rays. As the sun rises, the light becomes whiter and brighter. In the evening, it's the reverse, of course. So if you want those beautiful golden rays on the flowers, be ready to go as close to when the sun is just above the horizon as possible.
There are some very handy smartphone apps that will tell you--and often show you--where the sun will be at any given time at any location. Some even have a heads-up display that uses your phone's camera so you can see it exactly from the spot you're standing at. I have a roundup of these apps for tracking the sun and moon here.
Want to Help Support DC's Cherry Trees?
If you'd like to help support the care and upkeep of the cherry trees around the Tidal Basin, the Trust for The National Mall has launched an Endow a Cherry Tree Campaign. Donations go to the official Cherry Tree Endowment, which will give the National Park Service additional resources to fund the care, maintenance, and possible replacement of the cherry trees. You can find more information here.
The Trust is dedicated to marshaling private support for maintaining and improving the history National Mall area. I'm not affiliated with the Trust--just an admirer of their efforts.