If you have decided to go down to the Southlands to visit the Southlands Heritage Farm, then drive a few blocks south and take the opportunity to walk alongside the Fraser River. The Fraser River Trail is a super relaxing walk, with a view of a few boats in the distance and some planes flying in and out of YVR Airport.
The entire trail currently consists of four different parts, which are not yet all connected. However, the work continues to have this trail extending from Pacific Spirit Regional Park to the City of Burnaby's trail system! The part of the trail in the Southlands is referred to as Musqueam (since it sits in Musqueam First Nations territory) and can be easily accessed via Celtic Avenue or Carrington Street. The trail is pretty flat, so all levels of hikers are welcome and if you do get tired or simply decide to stop to admire the view, just take a seat on one of the park benches along the way. Bikes are also allowed on this trail, but bring your own as there are no rental places close by.
Especially on weekends, you'll likely run into other folks walking not just their dogs but also horses on this trail, which is a breath of fresh air from the sometimes more crowded trails around town. Also, with some luck, eagles and other wildlife can be spotted as well.