For a cheap hunt, you have to eliminate outfitters and flying. That leaves public land on places you can reasonably drive to. If I were in your shoes, I'd start by researching the public land opportunities in Nebraska, Missouri, Arkansas, Oklahoma, etc. I don't know which states have over-the-counter tags and which you need to draw, but I'd start with these because I know some of the others are draw only (Kansas and Iowa, for instance).

There is great public land hunting all over the country. You just need to do some homework and take your best guess. I killed my best buck ever this year on an out-of-state public land hunt, along with a couple of does. This was the first time I had ever set foot in this particular state. I called the Fish and Wildlife dept, I called various WMA's, I emailed / PM'd whoever I could find from that state on various hunting forums like this one. Some people ignored me, but most were very helpful and it paid off.

Good luck to you! It is fun and exciting venturing out to new places, doing the research and scouting and hopefully having it all work out the way you planned!