It's around a mile or so away, for walking, so this partly depends on your fitness, luggage etc.
There's a route here, from the McLaren Building, which is by the PC stop, which is 1.06 miles, according to multimap.com
http://www.multimap.com/directions/?qs_1…
Obviously you are not exactly at this building, as your starting point, but this is a useful reference point. You're heading for Broad Street, which is a busy nightlife district, (and has pedestrian walk ways via the central Birmingham library area, just off New St.)
As Birmingham city centre has plenty of one-way systems, a taxi would cover a larger distance, and probably not an awful lot quicker, say 5-10 mins. I'd walk with light luggage, and good mobility, as you're walking right through the city centre, and will get a feel for the place.
Hope this helps. Good luck! Rob