The Chattooga is an obvious first choice. With the rains we’ve had this spring the trout fishing might be pretty good, but June is pushing the limits on that river. Last summer, water temps were over 70 F by June 10, even in the very upper reaches of the flow. For trout, there are any number of small streams in the GA, NC, SC border area that should fish great, especially as you get more into NC. The lower sections of the Tooga are a good bet for red eye bass.
There are a number of impounded lakes within a couple hour’s drive. West into GA, find a string of small impoundments (Burton, Seed, Rabun, Tullulah Falls, Tugaloo, Yonah) leading into Hartwell. On the eastern arm of this complex in NC and SC, are Lake Toxaway, Jocassee, Keowee leading into Hartwell. I’ve never fished the eastern lakes, and fished the small GA lakes only a few times. The little GA mountain and foothill lakes are quite pretty—clear water, relatively little development—but I can’t offer you much advice on the fishing. Some hybrids have been stocked in Burton, but I’ve not heard of a consistent fishery for them. There are trout in Burton as well, but by June they will be deep. I’ve heard good things about the smallies in Toxaway. Black bass fishing can be quite good on any of those lakes, if that’s your thing. If you care to come down to the big lakes (Hartwell, Russell, Clarks Hill) I can offer up a few opinions on those—but mostly opinions on carp, I’m afraid. On these lakes, I find June to be a tough month for stripers on fly from a kayak. May be a few tucked up in the tailwaters, perhaps a little surface schooling from hybrids in the super early dawn, but for the most part, the stripey fish are deep.