Yes, exit 384, behind Steak and Shake. There's a McDonald at the corner too where you turn left.
Anyone coming from the north on I 75 will note there are 3 Gainesville exits.
The one to use for Red Roof Inn is Florida 24/SW Archer Road. (Exit 384)
Make a left turn at the bottom of the ramp. Go under I-75 to the traffic light at SW 40th Blvd. Make the left turn. Pass Steak and Shake. Turn left into the next parking area. Red Roof Inn is immediately on the left and very visible.
Get an answer from Red Roof Plus+ Gainesville staff and past guests.