Here's a few of the free sites I've used in conjunction with one another:
www.appannie.com - Keyword Explorer(ASO) monitor trends for your keywords and how they compare to other apps.
developers.appbrain.com - Apptimizer (at bottom under Developer services) ->Presentation. See how your keywords compare to other similar apps.
www.appkeywords.io - A keyword suggest tool (appears to scrape google play autocomplete)
Also use the tools provided in the Google Play Console. Store Listing Experiments and Acquisition Reports. With Acquisition reports you can see how people are actually finding your app including the search terms they used.