Heading straight for the SS Great Britain and the ships and cranes of the M Shed museum gives you a great grounding in the city's industrial heritage and a sense of how it shapes the present – allow at least half a day at both, more if you can. While there make sure you take in the Banksy art works in the area – his street art is another defining characteristic of the contemporary city.
The waterfront links the south of the neighbourhood with the old city. Eateries, pubs and bars line the quayside making for attractive places to eat by day, and a lively vibe at night.
The though-provoking We The Curious, a kind of creative, 21st-century take on a science museum, deserves at least a few hours of your time, the old city's shops and thriving St Nicholas Market, with its wealth of food stalls, are just a short walk away.
The Bristol Museum & Art Gallery is slightly further north – head here for Egyptian artefacts, dinosaur exhibits and another Banksy; you can take in two more of his artworks en route – the Castles Stencil and Well Hung Lover.
Central Bristol isn't huge, but you could end up walking a couple of miles end to end – a DayRider bus pass (£4.50) is a good option. Or hop on one of the services of the Bristol Ferry Boat Company. That way you get to travel and see this historic port city from the water – ideal.