If you’re staying near the Sydney airport (located 9 km south of the CBD), there’s a pleasant path along the Cooks River, which forms sort of a linear park. Marked as the Cooks River Cycleway, it’s not the most scenic trail in Sydney, but there are nice views of the water, and some wooded sections. The trail is mostly paved. One can do a loop of 9.2 km incorporating both the northern and southern banks of the river, but the south side path is more seamless. There are numerous opportunities on the trail to cross over.
The eastern end of the trail, closest to the airport, starts at Gough Whitlam Park on the south bank, near the Tempe Station (Line T4). Stay on the south bank It’s 2.2 km to Beeman Park, and 4.4 km to Sutton Reserve (pedestrian bridge crossing). If you prefer a loop, this is a good spot to cross over. Note on the north side there are a couple of on-road sections, and at Ewen Park you have to cross over to the south side briefly.