Avoid:
The bearpit and the area from the bearpit to the bus station. Moreso at night.
Stapleton Road from the bottom bit in St Judes to Stapleton Road train station.
The area between Stapleton Road station and Stapleton Road, especially at night. If you are visiting any of the eateries on St Marks Road, walk in and out along St Marks Road.
Lawrence Hill roundabout at all costs. Unsafe at any time of the day.
Lawrence Hill from the leisure centre to probably close to St George's Park
Broadmead and to an extent Cabot Circus unless you plan on visiting the same chain shops you could visit in any town really.
Bristol buses. Really don't get the X39 bus from Bristol-Bath unless you want to sit in traffic for a large amount of the way. Get the train instead.
Crabbs Causeway. People rave about this but again it's a shopping centre rammed full of chain retail shops. It's also a complete pain in the ar$e to get to and will involve a long bus journey or plenty of Bristol traffic.
Visit:
Do a ferry tour around the harbour. The 1 hour tours are really good.
Fabricland in Broadmead (next to Macdonalds) if you like fabric and sewing. Fabric galore. DH hates the shop because he says I spend wayyyyyy too much time and money there.
Clifton Suspension bridge (number 8 bus from the centre). Its free to walk across and if you're feeling especially brave, have a go on the rock slide next to it. Polished smooth by thousands of pairs of jeans over the decades.
Gloucester Road (75/76 bus from the centre or Redland/Montpelier train station). If you want something unusual food-wise then try the Ethiopian restaurant (Real Habesha). Excellent food and not overly expensive by Bristol standards.
Source: I've lived in Bristol for 40 years.