Well with no electricity, our handheld game systems would only last us so long, so our first step would be to get a power plant or two up and running. Also, we need food. Can't game on an empty stomach, I always say. Since it will take a while to get power back up, we'll have to keep our gaming sanity by playing Yu-Gi-Oh. Obviously we won't have access to the internet to find out the current ban-list, but we'll just keep the two Chaos cards & Yata out of any deck and call it a day. Board games would also work to keep our sanity too. In fact, Chutes & Ladders, SORRY!, and Yahtzee might very well be the only way to teach the future generation the fundamentals of basic life.
Once power is restored, we can create a grand Arcade again, where all can come to join and game. Of course, depending on the situation, we may need some kind initiation for those to get into Neo Arcadedia.