Susan, I was a volunteer for American Red Cross for many years. You will get fed at any shelter run by the ARC. Shelters are generaly in schools, churches, National Guard Armories and fairgrounds.
Any place that has space for a lot of folding cots and kitchen facilities. Shelter sites are picked ahead of time and factored into the overall Disaster Plan, so the School next to the chemical factory won't get picked. Some times shelter items like, cots, blankets, water, MRE's etc are pre positioned at the shelter site. Any other services such as medical aid, bottled water give away, etc are co-located. Shelter Management is a speciality within ARC with trained people to do it. For practice setting up a shelter is worked into disaster drills ,weekend "mini university" training days and apartment house fires also provide some practice. ARC actually has a well thought out training program. Initially you may get MRE's or food from local restuants, agreements with local restuarnts are made ahead of time. Life in a shelter is not great, but if it's your only choice it's O.K. No pets, alcohol, drugs or guns and not much privacy. And usually no showers. Generally, if you really don't need to be there, don't be there. Meals will also be driven out to the affected area in the ERV's (special ARC trucks). So people can eat while working to clean up their places. It takes time to get Mutual Aid from nearby ARC into the area, so PSK, BOB and 72 hour kits are essential. You might be told that you can't bring in a whole bunch of stuff, but nothing gets confiscated. As a matter of fact, ARC can only give out food that they have prepared. So all the cookies etc that nice people bring to the shelter get eaten by the ARC people, can't give it to the public since ARC doesn't know how it was prepared. The shelter people are happy when people show up with their own sleeping bags, flashlights, toy for child, etc. Hopefully the shelter has power or a generator, if not it's lanterns and flashlights. Whatever restroom facilities are there or porta potties. All these things go into sellecting shelters before hand and working the location, size, facilities available and access into the overall plan. Thigs tend to improve at a shelter as more aid arrives and people leave. That's what comes off the top of my head. Good question, thanks for asking.

Dave