I have the LL Bean 9' 8 piece fly rod that comes in a small tube and included the reel and line that's great for touring and back packing, I take it a lot. It's also the cheapest I could find that broke down small enough and had snake guides instead of foot guides, snake guides hold up better from accidental hitting of the guides. I prefer fly when touring or backpacking over spinning because it's more compact, the reel lays flat and you can hold a lot of flies in a fly tin.

You can get cheaper breakdown rods then the LL bean but the sensitivity is less as is the ability to cast well.
South Bend makes a 3 or 4 travel rods for under $50 including the reel.

You can also get backpacking spinning outfits as well. II bean even makes a backpacking kit that comes with both a spinning reel and fly reel with a breakdown rod with interchangeable butts so you can switch from one to the other. It's not as good of a rod as a dedicated fly or spinning rod, but it's cheap and you could fish both systems depending on your needs.