You agreed already. Swallow your pride, and live up to your word. If you're particularly nervous about the entire experience, go to a traffic-heavy area like City Halls or Courts. Malls are also functional as they have stores, people, and security everywhere.
Before you commit to a time, date, figure out your location and be aware of travel alternatives. Check for nearby subways, bus routes, parking, and taxi hubs. Once you have all routes known, you're set to get out if things go pear-shaped.
Make sure to keep everything public, in daylight, and plain sight. If you're still suspicious, make sure you arrive very early, and bring a face concealer like a newspaper or book. Sit someplace that's difficult to see, but you have a line of sight with the entrance to the meeting place. (For example, ask to meet at a cafe or diner, and sit at the store or coffee shop across the street and watch the front door.) Once you're prepared and you're feeling reasonably non-threatened, go through with your meeting.
If possible, pick the chair or meeting area closest to the closest available exit. Go just about everything as best you can. If you feel the meeting has gone wrong, politely excuse yourself. If that doesn't take, leg it. You have all of the knowledge and planning.
Of course, make sure you have plenty of spare money on subway cards, pocket change for cabs, enough for bus tickets, enough gas for a good distance, and your cell phone on you if it goes all to hell.
That's how I'd do it, if it were me.