If you’re looking for somewhere warm, Colorado is great in summer, but gets quite cold and snowy in winter (I lived there before nomading).
If your $1500 is just for housing, I think you’ll be totally fine in the US. When you’re searching Airbnb, just make sure you search for dates that span a month (this will switch them automatically to monthly pricing) and use the little pricing bar to select something under your budget so that you can see all the budget options. And like someone said above, always ask about discounts for a month-long stay, especially if you are there in off-season or want to stay for more than one month. My housing budget is less than yours and I almost always find something good on Airbnb.
Your other option in the US is Craigslist. Search for furnished short-term rentals (there’s a whole section for that). But be picky…you won’t have the reviews of Airbnb or the guarantee they offer (if you end up somewhere horrifying with Airbnb, they’ll help you out and get you into another place). I heard someone suggest once hiring someone on one of those online miscellaneous sites to go check out apartments or neighborhoods for them. Thought that was an interesting idea.
As for where to go, here are a few warm options:
San Diego, California: temperate weather, nice beaches, good Mexican food, not as expensive as people think (I rented a room there for about $700 if I’m remembering correctly, so I think you could find a small apartment within your budget). Downsides: as with most of the US, you will need a car and some neighborhoods aren’t as nice.
Tucson, Arizona: most definitely hot weather, an interesting city, again good Mexican food, cactus, hiking, hip university city. Downside: again, car, and people who have lived there a while say it starts to feel like a small town with small town drama (I’ve only visited myself, so I can’t speak to that).
Austin, Texas: Quirky, weird, great bar scene, colorful, great Mexican food, walkable downtown (you may be able to get by without a car - not sure). Downsides: Texas has that whole gun reputation that makes me personally feel nervous.
If you’re not stuck on the western US, I’ve heard great things about Charleston, SC.
Finally, I second what other people have been suggesting: consider going somewhere outside the US. Central and South America are cheaper, you can get by without a car in many cases, and the healthcare system is better and less expensive if something goes wrong during your stay. You mentioned being worried about not speaking the language - don’t worry about it! You’ll pick some up, people are super nice and ready to help you out, and if you start in a well touristed town you’ll find plenty of English speakers when you need them. If you do start researching this, I have a particular fondness for a town on the western coast of Mexico called Sayulita. Colorful, full of people from all over the world, a surfing paradise, a big yoga community, etc.
I’ve also heard great things about Costa Rica.