Hi Georgina, I'm sure you'll love Lyon. There are many parks and small greenery almost everywhere, Tête d'Or is only the biggest one and maybe the loveliest. You can also very quickly go out of the city and be in real countryside and in small mountains (Mont d'Or, Monts du Lyonnais, Beaujolais, Parc Lacroix-Laval). You can also go for a walk on the bank river (Rhöne and Saône) and there are a few "voies vertes" in some districts. Just look on a google map view and you will see a lot of green. Beside that, some districts are very urbans (6e but near Tete d'Or) and some very green and quite (point du jour 5e)...
Good luck...