For the drinks, coolers are the way to go. You can buy several (cheap) styrofoam coolers: 1 for beer, 1 for soda, 1 for kiddie drinks, etc. One poster mentioned marking them . . . great idea! Especially for the kiddie-safe cooler, draw some balloons (or use actual balloons) so the kids don't go digging through the other coolers.
If you really want to go the hamburger route and don't have a grill, I've had great success with hamburgers in the oven (not quite the same as grilled, but it works for large quantities.) Simply mix your ground beef with your choice of hamburger spices, etc. then press into cookie sheets, about 1/2 to 3/4 way up the sides. Use the deep cookie sheets with a 1 inch side (there will be grease, so don't pack the cookie sheet all the way full) . . . you can use the cheapy throw-away tin-foil type.
Bake in the oven at 350 for about 20-40 min . . . (sorry, it's been a while, I don't remember exactly how long it took to bake through. Check for doneness at 20 min.) Then cut the burger meat into serving-sized portions. True, your burgers will be square, but with two trays you can get 24 burgers (depending on the size of your trays and how generous you want to be with portions.) . . . It's kinda like cooking really skinny, flat meatloaf served on a bun.
If you want cheeseburgers, a few minutes before it comes out of the oven throw on slices of cheese.
Side note: when doing burgers like this, get the leanest ground beef available.
While the burgers are in the oven you can also steam or boil hot dogs.
Side dishes? The world is your kitchen . . .
Things to entertain the kids with? I love the time-capsule idea. Along with:
you got some great ideas.
for the kids - when i had a house with yard, i would just pick up some yard toys from a dollar store/sale items at dept store - things like beach balls, jump ropes, frisbees, paddles etc and let the kids play. Also - if you are OK with this - sidewalk chalk and bubble things.
for the cold drinks - as someone else suggested - an inflatable pool filled with ice.
Yeah. That's all you need. Simple stuff.
The best advice I have to offer is don't stress about being the hostess with the mostess . . . enjoy your friends, have fun, go with the flow and RELAX!