I chose a very specific location of Kansas City and SW Missouri on a four day schedule is doable from there. And southern Colorado is not out of the question from there either, based on a quick calculation. What I sketch out uses two days for travel and leaves two days for fishing:It cant be done on 300 . I just went to southern Colorado for a week and spent more than that on gas .
187.50 fuel to Beulah Valley Co, where trout fishing appears available within 15 miles (If you can get 20 miles to the gallon. I use S3.00/gallon as gas prices along the route today range from 2.63-3.23 per gallon). If trout aren't available there, they are at Pueblo, but back and forth adds 100 miles that brings it to $202.50
39.99 ultra cheap Martin fly rod kit with leader and some flies from Dickssporting goods
48.00 for 12 "brown bag" type lunches (based on a website estimate of what such a meal typically costs).
34.70 for two days of license and a habitat stamp
0.00 Dispersed camping for free in the San Isabel National Forest right next door.
That comes out to $310 and change, 325 if you have to drive to Pueblo each day. However, there's a free fishing weekend in Colorado each June. Fish that weekend and you can nix the license fee. That puts the proposed trip in the neighborhood of $275-$295.
The point is: fly fishing is far more in reach than people realize, even trout. You might have to be skinflint frugal and care not about your pride, but it can be done.
Have you got trout within 250 miles? Then my challenge is definitely possible.