Here are a few suggestions of alternatives to the Smokies. Sorry, but I don't know which trails do allow dogs in the Smokies. Once I found out about the policy I just started looking elsewhere. If Xena can't go, I'm not going, either:
At Big South Fork, try the Angel Falls Overlook. That's where the photos I posted are from. Here are details:
http://www.thebackpacker.com/trails/tn/trail_539.php
Also, the Leatherwood parking lot has a few other trailheads that are worth exploring. Water everywhere, so your Newf will love it. I don't hike anywhere that Xena can't go swimming.
Another suggestion is the Bowater pocket wildernesses. I just started hiking those, beginning with Piney River Trail, which was a really great hike. Again, no lack of water.
http://sites.gulf.net/yustaga/HIKE28.htm
And finally, my favorite place is Frozen Head State Park. Unfortunately, Tennessee is in a budget crisis and they've closed the state parks. But I'm hoping they'll be re-opened by this summer. Frozen Head usually has flowing water, though in the heat of the summer the creeks can dry up. I like it because the trails are really nice and there are almost no crowds.
http://www.thebackpacker.com/trails/tn/trail_503.php
Other suggestions:
Picket State Park (it wasn't affected by the state park closure. I was up there in December. Neat hikes)
http://www.state.tn.us/environment/parks/pickett/index.html
Cherhola Skyway: Wonderful drive, with several trails along the way to explore. Highly recommended.
http://www.westernncattractions.com/cherohal.htm
Tennessee is a great place to hike, and the people here are some of the friendliest I've every encountered. And I've lived a lot of places.