Here is a map that may help you find the places I have mentioned
http://www.idfb.co.uk/assets/map-738-600.gif
On the left you can see marked Repertory Theatre and Centenary Square. Just to left of them (partly cut off) is CC (for Convention Centre) and Symphony Hall.
This is where Brindley Place and Broad St are.
Also on the left you can see Gas St marked, and the canal alongside it. You can see it leads to the Mailbox (and there is a big red marker for MailBox).
At the bottom of the map you can see Hippodrome marked, and also the Arcadian next to it.
On the right of the map (big green arrea) is the Bull Ring shopping area.
All the Orange roads in the centre are banned to cars and most of the shops are in this area (mostly New St and Corporation St)