Muting Sonic Boom
This is an incredibly hard question and there is no answer, yet. Various techniques have been attempted but not have ever completely eliminated the sonic boom. The physics just won't let you. Better to go sub-sonic.
Check out these loiter times for unmanned drones:
MQ-1 Predator: 14 hours
MQ-9 Reaper : 14 hours (with munitions), 30 hours (without munitions)
Note that both drones achieve these loiter times by flying slowly. The A-10 achieves significantly longer loiter times over the F-16 simply by going slower. The faster you go the more energy it takes to overcome drag at higher speeds, ie, the faster you go the faster you burn fuel and the shorter a time you can stay airborne.
The drag equation indicates that the faster you go, that drag increases exponentially.
$F_D\, =\, \tfrac12\, \rho\, u^2\, C_D\, A$
$F_D$ is the drag force, which is by definition the force component in the direction of the flow velocity
$\rho$ is the mass density of the fluid
$u$ is the flow velocity relative to the object
$A$ is the reference area
$C_D$ is the drag coefficient – a dimensionless number|dimensionless coefficient related to the object's geometry and taking into account both skin friction and form drag.
Also note that $\rho$ decreases as altitude increases, thus explaining why the fastest planes always fly as high as possible.
Evading Enemy Fire
Unless you devote a large portion of your drone's sensors when flying at low altitude to detecting incoming air threats such as man-pads, SAMs or AAA fire, you're drone is going to be sitting duck. Devoting sensors to threat detection means that you have less space for mission sensors. The Reaper and Predator drones cited above never fly below 3000 meters over enemy territory because that makes them vulnerable to man-pads, SAMs and AAA. A drone specifically designed to counter these threats is not a recon drone, but a SEAD drone.
A drone version of the SR-71 intended to fly incredibly high and incredibly fast might be very compelling but that doesn't fit the OP's requirements.