Yes, the photos and video you could take of the cherry blossoms from a drone would be spectacular. But if you're tempted to fly a drone over the Tidal Basin--or indeed anywhere nearby--don't do it. It's illegal, dangerous, and the chances of being caught and prosecuted are excellent.
In the case of the Tidal Basin, there's a double whammy. Drones are currently banned from all of the 58 national parks administered by the National Park Service--and the Tidal Basin and National Mall area is one of those.
But more importantly, most of the Washington DC area is considered restricted airspace. As the FAA puts it: "The airspace around Washington, D.C. is more restricted than in any other part of the country." Special rules are in place that extend to a 30-mile radius from Reagan National Airport, well beyond the usual 5-mile limit from airports that applies to many other parts of the country. (And besides that, the Tidal Basin is well within the 5-mile limit of Reagan National Airport, which is just across the river.) The law might be controversial, but it's also enforced.
The White House is less than a mile away, and the Pentagon is only a couple of miles away.
And military helicopters use the Tidal Basin as a low-level flight path and pass directly overhead at very low altitudes.
Local military and law enforcement take a very dim view of drone violations, and the pilots who violate the rules are routinely prosecuted. There are also NPS rangers on duty who will catch you in the act.