Do not run SOOW into a breaker box or connect it directly to a breaker, big code violation there.
Run 10/2 romex to a box with an RV outlet, inside or outside the garage, your choice. Buy an RV extension cord to get the power to your rig when you need it. I've found that it's cheaper to buy a 30a RV extension cord with the molded connectors than it is to buy SOOW, male and female ends, and make your own. Unless you are going for a custom length like 35' or such. If you want to make your own, 10/3 SOOW (white, black, green) is fine unless you are going longer than 50', in which case 8/3 SOOW would minimize voltage drop.
I wouldn't worry about running it across the sidewalk, nobody is going to get electrocuted. It's more of a trip hazard than anything.
As others have said, what are you planning to run? If you want to run the a/c to cool it off and have the fridge on, you should be able to do that with a 20a cord. maybe try that first.