Mt Sivri (1749m) on the St Paul Trail makes a good day walk from Eğirdir. The 6km return trek to the peak from the hill village of Akpınar takes about 3½ hours. Organise transport to/from Akpınar, 5km from Eğirdir, through your accommodation or Eğirdir Outdoor Centre.
If you have a car, Akpınar is worth a drive for its viewpoint and teahouse overlooking the lake and peninsula. A return taxi from Eğirdir costs around ₺20. Also ask the outdoor centre about local walks and mountain-biking opportunities in the area.