There's a small low lying hillfort about 2 miles South (though it's mostly ploughed out, excavations in the 50's didn't get far, the site is water logged after digging down about a foot, so no finds.)
To the NNE about 8 miles is a suspected round barrow at Kings Norton.
A local archaeology group think they have discovered a Neolithic farmstead/community in the countryside outside Sutton Coldfield, though this was through field walking and field boundary analysis. No excavation took place (and if they did, i don't think they'd find much).
About 1/2 a mile away there are a series of' burnt mounds' in Moseley Bog, and more over in the Bournville/Selly Oak area (about 3 miles NW)
About 10 miles West there is Wychbury Hillfort, just outside Stourbridge. Morfe recons there's evidence of a couple of Long/Round Barrows, though i can't confirm that.
Nearest ritual landscape has to be Stanton Moor, Derbyshire about 50 miles north or the Rollrights about the same south. Though there are a few more hillforts, burial chambers etc not to far off in the Cotswolds.
So as you see they were right, the Birmingham region is almost devoid of any prehistoric archaeology. Finds in local museum seem to be only odd finds, several stone axes, flint scrapers & arrowheads.
A few hand axes/ palstaves scattered here and there. Seems indicative of people passing through (as most of the stone/flint sources are out of the region), no major settlements discovered (though the Romans did build a large fort (Metchley) a mile or so from the city centre (now buried under the School Of Medicine).
I guess the influx during the Saxon - Medieval period might have destroyed evidence of woodland clearings etc, though the region does seem oddly devoid of ritual activity. As you say, maybe they realised that Birmingham was a comin' :) (though to be fair, it's a lot nicer place than it's given credit for...just no good for a frustrated prehistory freak).