I prefer to reserve online and site-specific, but of course I've reserved at many parks by phone and "we'll find you a spot." They have in fact been perfectly fine.
I've noticed that if the park doesn't publish the current rate on their website I'm not very interested. If there's no website at all I get the feeling that they're out of business or don't want business and usually don't bother.
A website has been the primary advertising vehicle for at least 20 years. It takes zero effort. They could at least join the 20th century.
