The Hopkins River starts below the jagged peaks of the main divide and braids its way down the Hopkins Valley - a huge, glacier gouged affair with a wide, gently sloping gravel floor.
A four wheel drive track runs up the valley and makes for a slightly jittery but pleasant and easy mountain bike ride. After 9km you'll come to Monument Hut beside the river. You could stay there overnight if you wanted to ($5 hut pass from DOC). You could also continue up the valley to the next hut - Red Hut which you'd come to after another 6km and a few river crossings on a somewhat more challenging track. When you've gone as far as you want just turn around and return the way you came.
There are toilets at the huts and they normally have drinking water.
This trail is best ridden in summer but don't count on a relaxing swim - the river is shallow and cold. In winter you could have problems with mud in a few places.
Overall, it's an easy ride in a stunning alpine environment - the kind of place that will fill you with awe and remind you of the intransigence of life.