In the summer Deep Creek has a big tuber hatch for the first 7/10 of a mile upstream from the trailhead. It's hard to beat the crowd, especially on weekends. I've been out at 7am and they are out already. Same goes for late in the day too. As Art said, fish are catchable around the tubers, but it's not a pleasant experience. Due to the low water the last couple of years, they have moved rocks around in the creek to create runs for the tubes. This has disturbed a lot of the creek bottom and eliminated many nice holding spots for trout.
Take an easy stroll up past the confluence with Indian Creek (the tuber put-in) before you get into the water. The creek stays right by the trail.
It's continues to be an easy hike up to what's known as the turnaround, about 2 miles upstream, if you want even more privacy. It's a very obvious spot where the main trail takes off to the right up and over a finger ridge. You can get in the water there and fish around that ridge with nice exit spots before and at the first campsite. Depending on how fast you fish, 2 to 4 hours of solitude.