Look for lodging close to 22 Spokane Ave. in Whitefish in order to NOT need a rental car during your stay here! If you have a rental car, it opens up your options to Kalispell or Columbia Falls (~20 minutes from Whitefish), but honestly, Whitefish is the best place to be!
Tips: If you're search for airfare, do so on a Tuesday or Wednesday when they are the cheapest. Also, don't keep rechecking and rechecking from your same browser, as it will recognize you and that search and drive up the prices automatically. I (Mollie) am VERY well versed in booking flights, and am happy to find you the cheapest recommendation I can find!
Hopefully you won't need one! But if you do, all the rental car companies either rent directly from the airport (all the regular brands that you see at any other airport). You can also rent cars from the Amtrac station here in the middle of downtown. I know Hertz rents from there specifically. If you're in need of a ride from the airport downtown and back, I'm happy to help coordinate (me, Mollie) as I live here and can assist where necessary!