As previously stated avoid Belfast during the 12th July due to transportion disruption caused by Orange parades. Catholic tourists should avoid these parades due to their sectarian nature. In general tourists rarely have problems.
Never leave valuables, bags, passports inside a rental car in Belfast. Use a secure parking area.
Belfast - outside the immediate centre is a patchwork of neighbourhoods that are either Catholic or Protestant. If you see IRA; INLA; FTQ etc on walls or Irish murals you are in a Catholic Nationalist area. If you see Union Jack flags; UDA;UVF or RHC or murals with balaclavaed men showing moustaches you are in a Protestant Loyalist area.
Usually as a tourist you will be safe. Although there may be problems if you're overtly English in a nationalist area. Just don't go round shouting about colonial victories or Irish freedom unless you know who you're talking to. OK?