Once you've got an idea of how your camp is going to run, you're going to want to start getting kids on board. Before you can do that though, you're going to have a place to have it, so that parents can figure out whether or not they can bring their kids to your site.
Churches are an excellent resource (as are synagogues, temples, and other religious centers used primarily on weekends.) We found space our first two summers by calling up a ridiculous number of churches and asking around until we found a space that was free for the summer. Incidentally, this turns out to be a great to chance to refine your spiel about camp before giving it to families who might attend.
Small churches are more likely to be helpful than big ones. Religious organizations are almost always looking for ways to get involved in helping out the community, and bigger institutions are more likely to already be well connected, and, consequently, booked up, than small ones. In college towns like Boston, places that cater to the college community are going to be almost empty during the summer and are likely to be pretty enthusiastic about someone using their space for something cool.
Some religious sects have more hierarchy and bureaucracy than others. Unaffiliated churches are great. The fewer levels of bureaucracy that have to approve your use of the church, the faster you're going to get answers and the more likely you are to get good answers.
Schools are another possibility -- many are unused during the summer. Calling up the local school board or schools themselfves has never gotten me anywhere. Due to liability issues, only a few people in the school system actually have the authority to let a school be used by another organization. The easiest way to get school space is to either utilize or make a personal connection, who can then navigate the hierarchies of power to get your space use approved. I've heard some people recommend calling principals directly, though this hasn't really worked for us.
Getting cooperation from the local school system is probably something that you can get after you've done camp for a year or two and have some established credibility. We were eventually given space to use for Camp K one summer by the local school system and spent that summer in a school building. The next year we went right back to a synagogue -- there was too much arbitrary oversight, hierarchy, and bureaucracy for us to be entirely comfortable in their space.
Features to look for in a space include:
Being near a park or other play areas. If you're giving kids' freedom, you'll want to give them ample space to run around and play.
Being near public transportation. This opens the world up to field trips and the exciting adventures of taking kids on busses and subways!
Having parking nearby. Last summer we were in the heart of urban congestion -- Harvard Square, and there was no parking less than a 10 minute walk away. Whoever owned the street we were on (and how someone can own a street is beyond me) had hired a towing company to send a tow truck up and down the street we were on 24 HOURS A DAY. Counselors had to race outside out to fend off the tow trucks when a parent parked for three minutes to pick up their kid -- it was like playing Choplifter
Having more than one room to use. This isn't necessary -- we did without it our first year, but it can be really nice to have separate spaces to run activities with a small subgroup. We've tended towards labelling one area as the soft/quiet area, full of pillows, quiet voices, and chill activities, so that kids can escape the high-energy parts of camp when they need to.
And, lastly, people in charge who are excited about what you're doing. I can't stress this enough. If you don't think it's a problem for kids to run down the empty hallway on the way to the gym, but the people who own the space do, you're going to find yourself constantly having to enforce rules that you don't believe in. This slowly saps your credibility as well as your enthusiasm. If someone in a position of authority is going to periodically poke their head into the electronics take-apart area and tell you warningly that it's very messy, you're going to have a lot less fun, and be a lot less creative, than you would be if you felt able to use your own judgments.
Additionally, the site coordinator will want to know that you are going to be licensed, provide liability and accident insurance for the site, and are doing background checks on your staff. Licensing and insurance are contingent on having a site, but in my experience all the coordinators want to know is that you will get those things done and provide them with copies of the relevant paperwork once you have them.