Hey JJ, I had been tossing around the idea of a strategy game for when I have kids that's kind of similar to what you're talking about. I had thought of it as using a grid (wood parquet floor?) as spaces, and keeping it simple at first and then making it more complicated as they get older to help them think strategically. Hopefully my kids will like Star Wars...wait, of course they will.
Basically, you'd have "Teams", i.e Empire, Alliance, Republic, Separatists. Obviously it would be inaccurate to have the Alliance vs. The Republic, but if you really want to, what the hell. Within these groups you can have factions that have different skills.
For instance, the Alliance can have an Ewok squad that can set traps on any squares in the grid. The enemy can't see them, but you have to write the square's location down on a piece of paper when you set it, and obviously you can't change it unless you want to dismantle the original trap, but it still counts as a move.
You can also have Dresselians who can sabotage enemy machinery or snipe.
Gungans can form a deflector shield around your infantry and take out mechanized infantry with their boomer balls.
The Empire can call down TIE bombers to make precision strikes behind enemy lines.
Bounty Hunters/Assasins can be hired to take out leaders, which makes the troops less effective (still working on penalties for loss of leaders, but I know that an Empire team with General Veers should be better than an Empire team with a generic General)
Squads of Jedi can be used, but I'm trying to figure out a way to not make them invincible.
The Empire can send probe droids to investigate specific areas of the map.
These are just a few examples of what I've been planning. I'd keep it simple at first, for instance an AT-AT can fire once per round, and it can take out everything in a square. It would have a maximum and minimum range though, and I guess it would need to be severely handicapped to be fair. I'm also not sure how I would handle Hailfires and Gunships.
An outdoor game like you were saying would be cool. You'd need a bunch of line and a bunch of stakes if you wanted to make a grid for that though! Plus, your weapons might end up as lawnmower bait! Maybe asphalt and a chalkline?