Hi Rosy,
I knew Moseley Rd well right through the 50's 60's & 70's and I cannot ever remember there being a hotel of any sorts. All I can remember is Mrs Griffin's boarding house next to the library & baths. It was a theatrical boarding house where many up and coming stars stopped while appearing in Birmingham.
The building is still there today, but it is now a Sikh temple. The were of course small hotels & bed & breakfast places on Alcester Rd which is a continuation of Moseley Rd.
Phil