Run... took me six hours to get there once. Don't know the city center that well... so can't help but trying to understand to locals was a challenge. nice folk though, hope you find something. good luck.
Depends on what you like. The docks are pleasant. You can go see the Cabot Tower. Georgian House. There is or was an IMax conema, if it's still showing. Museums. Plenty of history but I'd advise getting a guide book. Is the Tourist Info place open ? Lots of restaurants. Shops.
There are lots of shopping centres Broadmead, Gallery's, and a newish one I think is called Cabot in the City Centre. There is an Ikea on the way out of Bristol M32 heading north.
Or there is Cribbs Causeway shopping mall J17/16 (not sure) of M5.
I only ever go to Ikea or the airport if I M visiting Bristol.
I'd get a ticket for the tour bus. I'd hop off at the Clifton Suspension Bridge, and at SS Great Britain - that takes an hour or so to look round, and then complete the tour to get the whole picure. End up back in the Old City for a look round some independent shops and cafes.