There are several options within a few minutes walk from Netherwood.
5 minutes walk or so along the canal (turn left out of the back gate) is The Cheshire Cat. This is a lovely traditional pub that has some nice outdoor seating as well as a cosy lounge and more formal restaurant area. Food is pretty reasonable and the menu is quite large. Dogs welcome in the lounge areas.
This pub is a right turn out of the canal back gate and about 20 minutes walk - head to the bridge at Waverton exit, turn right, turn right down Moor lane and then right again at the end. If you want to get there quicker, use the pavement next to the road, it's 5 minutes walk but not as pleasant! It is not too large inside but they have a really good all-day breakfast menu. They also have some nice outdoor areas, including some pods and tipis.
A slightly longer walk, about 20 minutes from the back gate (turning right is probably easier). A traditional family pub with beer garden and a decent menu. Dogs welcome in the tap room.
