Typically, off season events need room for a full field plus 30 pits (10x10). The specifics on the size of the area are obviously determined by layout... generally these events are held in high school gyms, so you can utilize bleachers for viewing the field.
Away from the space requirements, you'll obviously need a field. Sometimes these are team-built fields, others they are official FIRST fields (for example, you can
rent a field from AndyMark. Some areas, like MN, also have their own local fields available for off-season events). If you have an official field, you'll want everything - mechanical, electronics, an FTA, and game pieces. The FTA really is key, as they know the ins and outs of setting up, tearing down, and running the field.
In addition to that, you'll need volunteers. A lot of volunteers. Think of everything at an official event - queueing, scoring, field reset, pit admin, game announcer, MC, inspection (Yes, you should have inspectors there! At minimum a safety inspection should occur for every robot), etc. I think I heard that it typically comes out to 80 volunteers. Contact your local volunteer coordinator (whoever runs the volunteers at the regionals you go to) to get help with all of this, and do it early! I know here we start planning volunteers at off-season events 2+ months in advance.
Talk with your local regional planning committee chairman as well. They tend to know everything going on in an area, and can help out! They have contacts with all the local teams, and can get information about your event out there. They also know all about setting up and funding an event, so odds are they'll have some good advice for you, too!
Strongly consider timing as well. When will the event be held? Too early in the fall and teams won't started meeting for the year yet. You don't want to have the event conflict with anything significant in the area either (for example, a lot of robots are in the MN State Fair every year, so it would be bad to try to hold an event during the fair). Consider what teams will attend - will teams need to travel to get there, or are there enough local teams? If teams need to travel, what will the hotel availability be like during that time?
As for money required... most off-season events do have a per-team fee, and provide concessions as a fundraiser. The specific amount you'll need is obviously highly dependent on a large number of factors - space availability (do you have to rent the gym at school, or can you get it for free?), field availability, feeding volunteers (PLEASE feed the volunteers... it makes them want to come back again next year!), how much you collect from participating teams, etc.