if I was just getting off execution and was rescued
I'd get a long nights sleep at the local pub and then the next morning grab a bite to eat and think over all that Alduin and Grey Beards crap Esbern was going on about.
Whatever comes my way first as I start the game I suppose is what I'll do.
But most likely explore, or go to a city and check out how they work in this game. If they're truly open, NPC AI, shops, taverns, guilds, arenas, all that good stuff.
To be honest it depends where I am when I gain control of my character. (After the tutorial or whatever.) If I'm in the wild I might hunt or visit a village that is close. If I'm in a city I'll definitely begin exploring the city.
I will probably start by getting a feel for the game, get used to the gameplay. After that, I will probably go straight to joining a faction, unless I am preoccupied.