Best pram and baby friendly cafe in Durham city centre?

[Bemoremargo]

Any Durham people have any suggestions? I'm off to Durham for the day with my 3 month old to meet a friend (also with her 3 month old) and have no idea what to do! I'm still completely in a fog of sleep deprivation so would like to avoid aimless wandering! Close ish to train station and the river would be lovely, any ideas?

Cafe on the Green, on Palace Green is lovely, with views of the Cathedral and Castle. It's about 15 minutes walk from the station and a couple of minutes from the river.