Going to be running a demo night at my LGS. What are some good lists to run to highlight the game for a beginning player?

The one I was taught with, and thus use to teach others was

Rebels:

Red Squadron X-wing
Red Squadron X-wing
-R2-D2
- Proton Torpedo

Imperial:

Howlrunner
Mauler Mither
-Marksmanship
Backstabber

I used Rookie X-Wing and the 18 point Y-Wing with Ion Cannon and R2 Astromech vs the 21 point TIE Advanced and 2x Academy Pilots. Its 45 points each and plays pretty fast. Idea with it was to use all 4 ship types, but keep things as simple as possible, hence no unique pilots (and thier abilities) and no upgrades except for the Y-Wing which really needs the Ion Cannon to be useful and the droid to help its meneuverability. If you want to go extra simple and not do the full rules (no crits, no stress token, ignore the color of meneuvers) then you can drop the R2 and give the Rebels iniative.

Use the starter box suggested play list. The point vs points is not a match but the game does play out pretty balanced.