There is one at the springwater centre in hackenthorpe at 9.30 on a Friday morning which another mum told me is friendly although I've not been. There are rhytmn and rhyme sessions at beighton children's centre and also runaround play centre on a Friday morning (the latter is at 11am and is free entry for under ones but I don't find it somewhere you get chatting to other mums although my daughter likes the singing)
I imagine there are other baby groups at children's centres in the area, I still go to a breastfeeding one on a Tuesday, there is the nct group but that's in nether edge and (in my opinion only) seems more somewhere people who already know each other go to meet up..