You've moved to a great town for flyfishing!
Watauga is a great river and fishes well all through town.
South Holston is more crowded but is my favorite eastern river.
The best and easiest way to find the "low-down" is by visiting flyshops up there and getting river access maps. South Holston Flyshop is where I go.
The mountains above town have great brook trout fishing and the Nolichucky is good for smallmouth and some trout up high.
Upper reaches of the Doe fish good. I like Roan mtn. state park for the Doe.
The thing to remember about Sycamore shoals and other areas is: There are fish out the ying-yang but catching them is up to you.