Although your question is unclear whether you are planning to monetize your application or have already done so (which will allow you to go to work API or another premium option, but I think you need to figure out your own finances), I have the following suggestions for you .
I have used several APIs throughout my programming life, and when it comes to relative accuracy and reliability, the Google APIs were the best overall.
Unfortunately, the places API does not have a payment system with payment as necessary, for example, the referrals API, where we receive $ 0.50 for every 1000 over-limit requests. Google APIs can be very expensive for SMEs. This leaves you with only one glimmer of hope. This Google documentation suggests:
Free lifts for related applications
Having carefully studied this, I found this page , which sets out the exact requirements for raising, and I believe that it is very beneficial for you.
If you still think that you are going to use a different API instead of Google, I would suggest reading the this article, which provides a comparison between different APIs. (note that limit / price data may be outdated.)
Finally, when using different APIs together, I would use different services if they do not explicitly state that this is prohibited. However, the biggest problem here is displaying data on a map. Most providers prohibit you from displaying your data on another provider map or vice versa. read about it and in conditions. However, do not count on me or any other stranger for a legal opinion. Hope this gives you some idea.