I agree with the advice previously given.
I don't live there but I have several friends living in Harborne/Edgbaston with secondary-aged children. All of them sent their children to state primary schools (St Peter's, St Mary's, Chad Vale or Harborne Primary) and they were all happy with their primary schools (other than one whose autistic DS didn't settle at the very traditional St Mary's and moved to Priory.)
I know secondary feels a long way away, but @gldd makes a good point about considering it. If you have strong views against grammar schools and will definitely be able to afford private secondary school, it doesn't matter precisely where you live. However, if you even think it's possible that you might consider a state grammar for one or more of your children, it's worth making sure you're happy with your catchment grammar(s).
For example, if you really want a mixed secondary school, you need to live in the catchment area for Five Ways as that's the only mixed state grammar in the area. If you end up living just outside Harborne in Edgbaston, that's in catchment for the Handsworth grammar schools which many in Harborne consider to be less attractive (somewhat unfairly, in my view.)
The comprehensive secondary schools in/near Harborne are ok, but are not known to be particularly great (there might be an element of middle-class snobbery at play - I am reflecting the views of my friends.) Only two of these friends ended up sending their children to Lordswood Girls, and they are happy with the school. Most threw a lot of money and effort into tutoring for the 11 plus, and their children are either at state grammars (if they got in) or private secondaries (if they didn't.)
Of course, if you are happy to move in a few years, it doesn't matter so much.