I played a game at DunDraCon this past February, which had an approach that might work for you...
It was called the Dungeon of Chaos. The premise explained briefly why the place existed and why the PCs needed to do something about it.
A wizard had created the place to spawn random monsters for him to hone his magical abilities against... But he went missing and now the place is spitting out abominations that are threatening the countryside... The PCs were the short-straw drawers among the populace who had to go face off with this stuff and try to stop their creation.
Game play was structured around each level of the dungeon having three rooms (each with something to fight in it), interconnecting corridors with a trap at some point, a puzzle on each level, and the third fight was always a 'boss' (not my favorite term, but there it is). The DM determined all the layout, traps and room contents randomly.
So even he didn't know what we were going to fight at any given moment, nor what lay around the corner until we turned it, or listened, or what have you. Kept him on his toes, and might help make running a demo more interesting for yourself, as opposed to just running the same few rooms over and over...
In that game, even character creation was randomized, but I don't think that sounds too appropriate for a DCC demo.
But a "three-room dungeon level" might make a good demo, and if you like the randomizing approach, that could keep it interesting for you and for anyone that wanted to sit in longer than a fight or two... For that matter there are any number of 'dungeon generators' on the web and you could print off as many maps as you'd like, and randomly generate the contents from there...
Gnome Boy (a.k.a. "Jon") • DCC play-tester @ DDC 35, Feb 2011. • Beta DL 2111, 7:00 AM PT, 8 June 11.Playing RPGs since 1977
• Quasi-occasional member of the Legion of 8th-Level Fighters.—Here Be DCC Monsters—VOORAK, L, Hunter, S10, A12, Sm10, P6, I13, L15, AC 10, HP 3, Spear +0 1d8, Init 0; R 0, F 0, W -1, Holy water, Pelt, 3 iron spikes, 1d ration, 4-leaf clover (Find secret doors) (+1), Com +1
SARKLA, C, Gatherer, S9, A14, Sm14, P15, I14, L8, AC 11, HP 5, Knife +0 1d4, Init 1, R 1, F 1, W 1, Chest, Basket of veggies, 2d ration, lg sack, waterskin, torch, Seventh son (Spell checks), Com +1
TARR, C, Hunter, S14, A11, Sm15, P13, I8, L8, AC 10, HP 3, Spear +1 1d8+1, Init 0, R 0, F 1, W 1, Holy water, Pelt, 4 torch, flint/steel, 1d ration, sm sack, Fox's cunning (traps), Com
TELVA, N, Herbalist, S13, A6, Sm9, P6, I12, L10, AC 9, HP 2, Club +1 1d4+1, Init -1, R -1, F 0, W -1, Chain 10', Herbs- 1 lb., 50' rope, 2d ration, torch, Speed of cobra (Init), Com