Can anyone Manchester think of any green spaces less likely to be dogs

It’s not uni related but thought it’s worth asking. I live in Ashton, Tameside and love nature but have a bit of a phobia of some dogs.
I’m not familiar with south Manchester but I wouldn’t mind travelling to areas round there.
I like sunbathing on a field near Henrietta street which seems less popular, I think because only the people who live there have heard of it. Can anyone think of any more areas like that or reservoirs etc where no one really visits?