Prices and availability of rental cars will vary considerably depending on demand. If demand is high for a given period, prices will increase (sometimes significantly!) As you get closer to that point, and individual locations may be exhausted. If the demand is low, prices may go down as you get closer to the date.
Generally, the best option for someone in your situation is to make a reservation that allows you to cancel without charge and then keep an eye on the prices as you approach the hour. . If prices go down, you can cancel your existing reservation and create a new one. If it turns out that you do not need the car, you can cancel the reservation without charge.
Since you are not from the United States, if you end up making a booking while you are physically in the United States, you must make sure that your home is properly selected on the site from which you are booking. . If you do not do this, the required insurance will not be included in your booking and you will have to pay for it at the pickup, which will significantly increase the price.