Bus routes from Birmingham New Street

[Harlesden]

Got two hours to kill between arriving 07:45 (weekday) and catching my connecting train at 10:03. First time in Birmingham, don't want to get lost.
I was thinking of either a circular bus route serving the station or else a high frequency route like every 5-10 minutes to/from wherever.
I'd rather spend £2.10 on a Birmingham Plusbus than be walking around aimlessly in a totally unfamiliar city for two hours.

 

[WestCoast]

Lots of choice but I'd recommend two nice bus corridors from New Street, leaving from Smallbrook Queensway just outside New Street (follow signs for Bullring from inside the station). I might be a bit biased as I live in this part of the city, but these are two lovely and quick runs from the City Centre.

-The 99/98 out to QE Hospital/University is a nice run through parts of the City Centre and then onto leafy Edgbaston streets with combined service at least every 10 minutes. It mirrors the train route from New Street to University. Alight at the University or QE Hospital. About 15-20 minutes ride. Leaves from Stop NS3 outside Boots. If you're short for time you can catch the train back from University direct to New Street in under 10 minutes, but it would be highly unlikely that getting there and back would take longer than an hour.

-The 22/23/24/29 towards Harborne also a nice run taking in parts of the City Centre (Mailbox, New Library, Broad Street etc), Edgbaston (Botanical Gardens) and then Harborne High Street. You can go further but I'd recommended alighting at Harborne. Combined service approx. every 3-4 minutes. About 15-25 minutes depending on traffic. Leaves from a tempoary stop a bit further down Smallbrook Queensway. Takes a different route back into the City Centre so you get to see quite a bit, some journeys are hybrid deckers.