Cost
Venue sponsorship should be just that: sponsorship. That means the venue should almost always be free. It's occasionally ok to pay for a venue, but that's usually limited to covering a cleaning or heating cost of less than $300. If you're expecting to spend money on a venue, you should be confident you can offset it with additional sponsorships.
Be aware that many "free" venues have contracts requiring use of specific companies, like hiring their A/V contractor if you're going to use a projector, or ordering food only from their specific caterer. The cost for these locked-in contracts is usually way out of the event budget (Microsoft's contracted caterer charges $14 per person just for breakfast cereal). This is usually only an issue in larger buildings, but it's worth asking about and, if there are any requirements, asking if the company will cover the cost as part of the sponsorship.
Size and Layout
Your specific space requirements will depend on your expected attendance. For new, smaller cities, a venue might need to hold 60 people, while a large, established city like Phoenix will require space for 300-400! Remember, as well, that you'll need to have a space to hold all these people (standing, if necessary) for the kickoff and awards.
For larger events (above 120), it's best to have multiple rooms into which you can subdivide the event. Having more than 120 people in one room makes it much less likely that participants will meet people from other teams: it's simply too big.
The layout of the rooms is also important. Venues with a few big rooms are preferred to those with lots of conference rooms. The goal of CodeDay isn't just to make something cool, it's also to encourage a community, and it's hard to build a community when people lock themselves in a small room. (If the venue does have lots of conference rooms, can you close them off for the event and still have space in the main rooms?
Location
The location of the venue is important, but we don't mean look for "a good neighborhood." A primary goal of CodeDay is getting students from non-typical backgrounds interested in code, and many of these students don't live in the urban core.
Good access to public transportation, plenty of on-street parking, and name recognition are all things you should look for in a venue.
Hours and Age
The venue needs to be available for 24-hours, which might mean the venue needs to find staffing for the full weekend.
It also needs to allow students who are under 18 to attend. This is often a major sticking point for really large organiations (particularly universities), so it's worth double-checking -- we've had problems in the past.
Tables, Chairs, Whiteboards, Outlets, and Wifi
This might go without saying, but the venue should support the expected attendance with tables, chairs, wifi, and distributed access to power.
Organizers occasionally select a venue which can't support the full attendance; in this case you can rent tables and chairs from a party rental company, and borrow power strips and extension cords. This isn't cheap (usually $300-600 to add seating for 100 people), so it's usually a last resort.
If you're just a little short, you can ask attendees to bring any folding chairs they own in a pre-event email.