The Macquarie River is a feature of Dubbo. There are walking tracks, cycle tracks and parks along both sides of the river. At the west end of Tamworth Street there is a car park and walking track along the river out to the Zoo which is very nice.
Here is a picture of the start of the walking track at the bottom end of Tamworth Street.
If you want a picnic by the river, check out the West bank of the river, behind the West Dubbo Bowling Club. From the main street heading south, turn over the bridge, then left at the roundabout, towards the Zoo. Turn first left after the West Dubbo bowling club, into a little steep road that takes you down to a picnic area on the river bank with shelters and a BBQ.
Otherwise there are many places just to sit and enjoy the birds and the river.