I'm just back from Belfast and if you're out for electricals or furniture, there are limited opportunities in the city centre. I could only find two tv shops in the centre - Richer Sounds at the back entrance to Castle Court and Currys down the road, and neither had the tv I'm after. For furniture, there's always IKEA out by the airport which is amazing, but expect to spend a few hours there as it's massive (they deliver to the south, but the standard charge is £150 for 2 trolleys worth of stuff, and another £50 per trolley load after that).
If you're mainly heading for Argos, somewhere closer to the border might be easier to get to. Newry is a pain in the **** to get out of, so Lisburn might be better.
The best advice I can give you for getting about to make the most of your time is to get hold of a sat nav (beg, borrow or steal) and program in the places you want to go to in advance - it will save a lot of stress.