If you want to go for a run from the city centre you could start at the canal, next to the magistrates courts and follow the towpath to castle marina and further towards Beeston , it is perfectly safe.
Or you could run down parallel to the tram tracks past Nottingham trent university, towards the Forest recreation ground (not the Nottingham forest ground, that is in west bridgford) and have a good run round there, it is safe during the day.
Or you could head south towards Trent Bridge, this will take you past the Meadows, but it is fine during the day, and to the River Trent which has a nice embankment area to run along and you could follow it to the end, run back along Castle boulevard.