We have great coffee houses and restaurants close by ... so if you need to show your customer arround, then you have all opportunities.
Graz has about 45.000 studends and therefore the nighlife is quite vibrant.
In the center of Graz your car can be halted on the street for 10min. for free and parked for 3h at a charge of 0,90€/30min. Ticket machines are always close by. There are controls - so don't park without paying!
Graz has a fairly good public transport and so you can leave your car on a Park & Ride parking lot or put it into a garage - further information can be found here.