Keep in mind that you can also use Amazon Coins to pay for in-app purchases. I'm pretty sure that this only works when you install the app from the Amazon App Store.
"In-app purchases" usually brings to mind game add-ons or credits, but some apps are only available as free downloads and you have to use an in-app purchase to unlock full functionality or to turn off ads. Something else you might try is paying for subscriptions in-app with coins. I've never tried this, but if you use apps like Pandora that have subscriptions - can you pay in the app using Amazon Coins?
I got
Monument Valley for free (usually $3.99 - a good puzzle game) a while back, but I liked it enough that I bought the
"Forgotten Shores" add-on for additional levels via an in-app purchase for 199 coins.
Reference apps are a good way to use up coins quickly. For example:
Audubon Birds Pro: A Field Guide to North American Birds $3.99
A nice graphing calculator app:
Graphing Calculator by Mathlab (PRO) $3.99