In the USA in general, clubs do have the recrprical policy of allowing guest members to play their courses. Let your club pro know where and when, and they will make a call to the course's pro and set that up. You will have to pay their full rates, so this is not a cheeper solution, in fact it is more expensive because you are still paying your club dues. But you are now open to play the private courses if you have the money.

If money is the constraint, learn to love your course.

If you can't join a club, learn to play the public courses at the right times...like the weekdays. Get to know that pro and the staff taking lessons and just hanging around. They love to break the monotony from that job. You start to build your own repore there...kind of like having your own club. Then, you might get invited to play in the tournaments that could be at the private clubs.

In general again, I do not think it is in any clubs interest to allow mambers of other clubs to simply play their course without paying extra...if that was the case, everyone would join the cheepest club and all play at the nicest.