Hotels in Birmingham city centre with car parking are rare. I’ve used the Copthorne at Paradise Circus many times and found it to be discreet and lends itself to the kind of daytime meets that we all enjoy. There is a car park within walking distance, less than 100 yards. I think it’s called the Civic Centre car park and is behind Baskerville House.
If you want parking and something closer along the A45 then the Holiday Inn at the airport would seem to fit the bill.