Here are some with at least free tiers:
MapBox has 50K pre transactions per month
MapQuest has 15K/mo
Here.com (formerly Bing Maps) has 250K requests per month.
and OpenCageData has a "free trial" with 2,500 requests per day, though it appears you have to sign up to find out what is meant by "free trial."
Also note that Google Maps still has a $200 monthly credit for each billing account, after the 1 year of free transition time:
For each billing account, a monthly $200 USD Google Maps Platform credit is available and automatically applied to the qualifying SKUs.
For each use of each API you can see in these tables a column called "$200 MONTHLY CREDIT EQUIVALENT FREE USAGE" which shows how much usage falls within the monthly free allotment. It's complicated and you have to go through the tables and compute how much of each service you think you'll need. However for many use cases you can still end up using these APIs free. For now, anyway.