A lot of companies are well-equipped (over-equipped?
) with gas-powered things like chainsaws. You would probably want to bring your own saddle and whatever accessories you climb with like carabiners and eye-eye splices. Ropes are heavy and bulky, so you may be better off buying one here for $60.
What I mean is, you should bring whatever is very personal to you and don't worry about the rest because it's not worth it. Many companies will have a spare saddle, but is it something you would want to use? I'm not sure what your plan is, but it would be hard to find someone who would be very generous if you just showed up, planned to stay only for a little while, and wanted to use all of their stuff.
But no worries, mate! You would be better served with some of your equipment and a willing attitude to help wherever is needed, climbing if they have an opportunity for you, and building trust with them over a brief period of time. Some of the guys here might be interested in a recreational climb and perhaps something more serious and work related. I think in this industry like any other, it's all about building trust with a solid track record.
Good places? The redwoods... the Pacific Northwest (Oregon, Washington) have beautiful forests. You'll find trees across the country, but if you're able to, see the coasts if you can. Stay in between the coasts for a while to save money and get to know people.
Bark twice if you're in Milwaukee.