I think Birmingham has many fine buildings, worthy of being called landmarks, but unlike London, we don't tend to show them off or use them in publicity to attract people to the city or even help dispell the idea that Birmingham is a concrete jungle which most people who haven't been here tend to think it is.
Here are my suggestions, sorry I do not have any photos.
St.Paul's Church and St.Paul's Square
The Grand Hotel
Birmingham Eye Hospital
Baskerville House and Hall of Memory
Moor Street Railway Station, particularly inside.
Digbeth Police Station
Clock Tower, Jewellery Quarter
Old Joe Clock Tower
Great Western Arcade
Old Assay Office, Jewellery Quarter, particularly inside
Hockley Cemetry Catacombs
The building, corner of Steelhouse Lane and Corporation Street, the closest thing we'll get to a flat iron.
Most old tram depots
There are buildings less than a 100years old, which are very pleasing, these include;
Alpha Tower
The Cube
Colmore Gate
Fort Dunlop
New Library
Wesleyan Tri-corn building