AC doesn't reach my room so it appears that I'll have to buy something separate. I am looking for something that is quiet as I can't sleep with too much noise and cheap (under $50). Any recommendations from places like Walmart or Bed Bath & Beyond?
Here's what I am doing. The window AC is entirely optional, I very seldom turn that on (maybe 3-4 times a year for an hour):
My bedroom is upstairs, which is always a fair amount warmer than downstairs. Spring through fall during the evening and night hours it generally remains much warmer in the bedroom than it is outside.
That air conditioner is obviously more than the $50 you are budgeting for this. It cost less than $110 at Lowes. I also bought a cheap fan off Amazon, I'm not using that. I have a couple of big box fans I found or a past roommate left in the house that I used to sometimes (rarely) jam in an open window in the room to cool it down on the hottest of evenings. I never do that now.
I'm in my bedroom right now and those two computer fans are on, there's only a hush of noise.
The 200mm computer case fans are mounted in a rectangular piece of thin plywood (cut out holes for the fans). I have that mounted in a partially open window in the room right next to the seldom used air conditioner. The fans are powered by a 12v wall-wart with sufficient watt rating to support the two computer fans (I had that, I save old wall warts, figuring I may have a use for them one day). That's plugged into an extension cord that has a switch on it. The switch is right next to my bed, secured to my night stand. I can turn the fans on/off in an instant. The fans bring in cooler air from outside. It costs next to nothing in terms of electricity. The fans cost around $16 each. One developed some noise (they are extremely quiet "silent" fans), and I lubricated it, problem solved.
Cooler Master MegaFlow 200 - Sleeve Bearing 200mm Silent Fan for Computer Cases
I have the fans on at night, around 1/2 the nights during the warm part of the year. Last night I had the fans on and turned them off during the night when it had become fairly cool. I often turn the fans on 1-4 hours before I go to bed in order to cool off the room ahead of time. The cooling function of the fans works best with some time, it's not as quick as an AC. In general it cools the room, I'd say, around 6-7 degrees F compared to what it would be otherwise, given a few hours.
Just in front of each fan I installed some fairly coarse (i.e. not fine) screening I picked up at a hardware emporium (they sell it by the foot). It's fine enough to keep out mosquitoes, flies, moths, etc.
The two computer fans are 20x quieter than that roaring AC unit! Also, way way cheaper to run (not just the initial expense but also the electricity, which is pretty negligible).
Without the very optional AC component, you could do this for under $50. The AC actually makes it less efficient because that space could be just screened space that would let in more air from outside.