[tallytarik]

We self-host nominatim as part of the iplocate.io pipeline. It works great, but the requirements are pretty heavy for something to host casually.

An in-between for OP could be something like opencagedata.com, which is still a third-party API but an order of magnitude less expensive than Google. (not affiliated but have previously explored the service)

[cyberax]

Komoot is also available (I linked it), they have a rate limit of 1 request per second, but it should be enough for personal use.