I was thinking about heading south too.

Weatherspark.com
The weather will be quite variable in late March. It could be cold and damp or hot and sunny. I use weatherspark.com to check averages and see previous year's history graphs. Each city has an Averages page with temperature, wind, rain, etc charts. The Dashboard shows both previous years actual weather and the coming forecast. You can use the slider to squash the graph narrower to browse history easier.

Yearly Averages example. I forgot what city this was from.


Actual history chart. This is Cincinnati OH during the unusually cold winter last year. We had some very warm days in March, and some extremely cold days.
The shaded red areas are the range of highs by percentage, and each day shows as a bar.


Places from north to south.

Cincinnati OH. (My local area.) It's not spring yet, expect to wear gloves, tights, and probably a jacket. But there can be some very nice days to ride. It's just unpredictable. The April 1 average high is 60F/16C, but it could be way higher or lower.

Route 8 along the Ohio River is a nice ride, small rolling hills and not much traffic. Route 8 West is 40 miles--I rode that on Saturday. Or 60 miles Route 8 East to the old river town of Augusta KY. Or go climb the hills away from the river. The hills are 300 feet / 100 meters around here. There's a lot to do after the ride in Cincinnati.

Lexington KY. Too far north for dependable warm weather, but you have some last-minute flexibility you could pick some warm days. The rolling country south of Lexington is scenic with fancy horse farms, and miles of dry-laid rock fences.

London KY puts on the Redbud Ride in late April. Around here, the redbud trees are blooming when most of the other trees are just starting to break out of winter, so that's early springtime. Some local riders did this ride last year and liked it. It's a small country town. The area looks like rolling hills, most under 300 feet / 100 meters, and quite rural. It actually doesn't look "that" much different than the hills on the Kentucky side of Cincinnati. It's not really worth the drive for me--I would keep going south to bigger mountains.

Knoxville TN. I've driven through there a lot, but never stopped. It looks like there's hills out of town. It should be fairly warm there.

Chattanooga TN has the 3 State 3 Mountain ride in May every year. The climbs don't look too difficult on the route maps, around 1000 feet / 300 meters and an average 5% grade. The first one is 1400 feet, 4% average. There's a lot of non-climbing riding there too.

They are pretty far south, almost out of Tennessee. And at least 5 degrees F warmer--see yearly averages. April 1 has a 68F/20C average high. It's a long way from Canada, but might be worth the drive. I've never been there.

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Taking I-40 from Knoxville:
I like to go to Asheville NC, and ride the Blue Ridge Parkway. It's probably no farther than Chattannooga. But it's very cold up at the high elevations. Even in early May, it's often cold.

I thought about going to Greenville SC. It's a low enough elevation that it should be warm, with a April 1 average high of 68F/20C. And there's mountains nearby if I'm in the mood and it looks like a nice day.

The Ceasars Head climb is on this route: 63 miles/100km, 5900 feet/1800 meters.
Or lots of small rolling hills: Covered Bridge ride.