Here is what I would do if I did not have an "in" wife and a mother in law that would be ticked off by my actions bellow.
First lets assume a few things...
1- It would not be a race to see if I can make the device smaller and smaller. It just need to be stealthy. Assemblies are full of lunch boxes and briefcases. I got space to work with so I would not short change myself and sacrifice in other areas.
2- I would not expect a whole lot of users to hit the device at once. There would be no streaming from this box and I would not be sharing a public internet connection.
3- In my view, the name of the wifi SSID is irrelevant, in fact, the more innocent it looks the better.
4- I would not want to seat at the assembly all day and have to listen to the crap if I don't have to.
Content Server: As proposed here, a Raspberry PI is a good platform to serve your content from. It can run your web server, DNS, DHCP and provide tons of storage for whatever content you want to dump on it. It provides the flexibility of making changes to the software, content and other features you may need.
Wireless connectivity: A PI and be fitted with a USB wireless adapter but those tend to have low transmit power and weak antennas. I can find a USB adapter with an external antenna but I believe there are better solutions. Using a standard wifi router would provide much better coverage. It usually has more diversity built-in so it means more antennas are there to catch signals. Now lets not be misguided, just because a router has 8 plastic prods coming out of it, it doesn't mean they all actually work. Never the less, a wifi router has better diversity and more transmit power, period. I would pick one that has removable antennas so I can attach my own. I could also serve my content from a router that runs DD-WRT. This would not just give me the flexibility to configure WIFI in a way the gives more coverage, but also reduces power consumption and complexity of the setup. The con is that it may limit storage capacity and I am not sure how efficient a web server can run in such a small router. I guess I would have to experiment.
Power: The PI only consumes about 2 Ah and a WIFI about 1 Ah. Assuming they are always running at peak power, we are looking at a total power requirement of about 3 Ah. A 20 Ah battery can be had for $40 dollar. At a size of 3x6x7 inches (found one in Amazon) it can be fitted into most lunch boxes, laptop bags or whatever bag my nice JW side of me would have picked to take to an assembly. This would give you a run time of about 6.5 hours if not more.
Antennas: Here is where not being limited by the size of the setup has its advantages. There are several ways in which you can build or install a high gain antenna into your lunch box or briefcase. This is where the most of your coverage would come from. Wether you simply buy a high gain omni antenna and stuff inside or build your antenna into the sides of the bag, briefcase covering, etc. I could even look into aluminum briefcases. While it would not be better than a copper antenna, the shell of the briefcase itself could be the antenna. Not the best material but may be the gain in exposure would make up for it
WIFI config: Asides from the standard stuff that I would have to configure, I would look into other settings that would help out with the coverage. Not having access to manage the end devices puts some constraints in my setup but things like reducing the channel to 20 MHz and forcing all devices to use a single band, like 802.11n would increase the efficiency of the AP while the narrower channel makes the devices more sensitive.
Content: I would leave that up to my wildest dreams and change it based on the theme of the assembly.
Personally I would just walk in, find a good seat, hopefully located towards the center. Drop the suitcase or bag in place, wait a few minutes and walk away. Leave some books and a coat behind. Get on my car and go about my day. At the end of the day I would pick it up and take it home to recharge.