There are lots of different ways to discover the old town.
One suggestion is visiting St. Peter's cathedral. There is a magnificent panoramic view of Geneva waiting for you at the top of the cathedral tower. Beneath the cathedral you will find the fascinating archaeological site.
The 'Maison Tavel' museum is an absolute must to see some very impressive scale models of Geneva as well as the impressive 'Hôtel de Ville, with its beautiful interior courtyard. Finally, there is always the very pleasant option of sitting down to have a drink in the old town square, Place du Bourg de Four.