I've thought of another two high spots, not far from where you live, Relisys.
Head up Coventry Road to Wagon Lane, Sheldon. Go about a quarter-of-a-mile down it and you'll come to some grassland on the right. Make your way down to the far end of this and you'll see that the land on the right-hand side rises sharply; there might be a decent view of Sheldon, Yardley and Acocks Green from the top.
In Small Heath, near to the Blues' ground, there's Kingston Road and it has some high parkland on its north side, overlooking Small Heath, Bordesley, Duddeston and the City Centre. The Council have built a cute henge on the top of the mound and it might be possible to stand your camera on top of this, obviating the need to lug a tripod up there.