Re: Public vs. Private land.
A good start sometimes is to stick to areas that are proclaimed as Fly Fishing Only waters by the various state board of fisheries. Consulting the regulation booklets usually will clearly define those areas for you. These areas usually hold fish although the fish sometimes possess an uncanny skill for being able to discern between naturals and our imitations.
If you simply are driving and spot a likely looking stream that borders the roadway the best bet is to wait to spot a public access parking area. These methods may not yield the best results as far as solitude or quality of fishing but will keep you out of trouble. If your wallet can support it, hiring a guide out of a local fly shop will sometimes open up a treasure trove of areas that may in fact be open to the public but off the beaten path enough that you would never find them while just passing through.
If you have fishing at all close to home I would say to take a good close look at those opportunities prior to crossing the country looking for Valhalla. Some of the best places I've ever fished were close to my homes in various states where I have made my home. Many times anglers pass the obvious while they are caught up in the headlong rush to get to some highly recommended spot. Those are the places where you will often find people like me, those who want to feel that they found some hidden gem.
Good luck and by all means if you find your own little piece of heaven, don't advertise it!