Weston Park Museum is well worth a visit:
http://www.museums-sheffield.org.uk/museums/weston-park/home
(I visited Sheffield during my 6th form days to view the college I was considering attending after leaving . It was probably finding Weston Park Museum that made me decide that Sheffield was my first choice!)
The Millennium Gallery also looks interesting:
http://www.museums-sheffield.org.uk/museums/millennium-gallery/home
(I can't comment directly as it wasn't even there during the 20 years that I lived in Sheffield.
The neighbouring Winter Garden (right in the city centre) could be a good place to go for a coffee:
https://www.sheffield.gov.uk/out--about/parks-woodlands--countryside/gardens/the-winter-garden.html
Meadowhall Shopping Centre is easily reached by bus, tram or train:
http://www.meadowhall.co.uk/
Kelham Island Museum is fascinating:
http://www.welcometosheffield.co.uk/dms-connect/search?dms=13&c1=front&GroupId=2&venue=1581195
and provides an excellent excuse for visiting the Kelham Island Tavern
http://www.kelhamtavern.co.uk/
which is the only pub ever to have been awarded 'National Pub of the Year' by CAMRA for two consecutive years.
See here for further ideas within, and around, the city:
http://www.welcometosheffield.co.uk/visit/attractions