Having also sprained an ankle in the last few months, here's my opinion...
First, I sprained mine playing football in the 2nd series of the game. Taped it up and went on to play (sort of, playing center I ended up on the ground nearly every play) up until the end of the 3rd quarter. Trainer put ice on it, elevated it, etc. I couldn't walk for 12 hours.
Went to PT Monday morning walking real slow. We did some circles, ABC's, and the trainer reevaluated it before ice and stim. No contact, no weights! Went to see doctor that day, got x-rays and PT script. Spent the next 4 days in PT for at least an hour. Played football just over a week after spraining it. Continued PT for another 3 weeks while starting basketball after a week break. I get my ankle taped every day for basketball practice; I hope I don't have to for baseball as well.
Here's what I did with the ATC and PT:
Theraband exercises (sounds like the surgical tubing maybe)
ABC's, Circles, ankle pumps in whirlpool
Circles, ankle pumps, and side-to-side stuff on a balance board
bike and elliptical
throwing ball against trampoline while on two balance balls
trampoline exercises
calf raises on a half-ball
ultrasound treatment (two or three times)
line jumps
Then we got into functional stuff like shuffle, one-legged hops, two-legged hops, jumping, running, and simulated landings from elevation.
After each treatment session, I did ice and stim for 15 minutes. Also, I would typically ice at home as well two-three times a night.
When I get a chance, I'll put up a link to our local clinic's website which has an ankle-strengthening program on there..