Hi there Georgina!
What are of town will you be staying?
If you are downtown, the Scioto Mile or the olentangy river trail are two great waterfront areas that are easy to get to. The olentangy river trail goes 13 miles up into the far northern suburbs so you should be able to hit that up Jo matter where you are staying.
If you are on the North side, I would suggest high banks metro park as well as blendon woods.
East side of town I would go to New Albany and the country club has beautiful paths worth using.
I hope this helps!