More people want to see a return to school and work before pubs and restaurants are reopened.
But half of those polled by public health experts say the 2km limit on travel is the lockdown measure they want rid of first.
Researchers at NUIG, GMIT and DCU polled over 35,000 people for the Corona Citizens' Science Survey about the impact of the pandemic on daily life in Ireland.
Epidemiologist and joint research lead Dr Akke Vellinga says if it was possible to lift the restrictions, the priority for people is getting out beyond their neighbourhoods.
"Most people said they wanted to see the 2km restriction relaxed first.
"In second placed it was the small group gatherings.
"Going back to work and going back to school were in third and fourth place."
