What are the best acquisition channels for apps outside of Facebook and Google?

You can check the Appslfyer Performance index, where you find the best-performing ad networks split by geo, category, and platform, or Singular ROI Index

There is a whole universe of acquisition channels that can be effective for your app depending on what kind of traffic works for you / what your audience is.

Other Owned Inventory Sources / Self Attributing Networks

Snapchat, Amazon, Pinterest, Twitter, Oath, Tencent Social

Rewarded Video (SDK traffic)

The "top tier" here is Unity Ads, Applovin, Vungle, ironSource

DSP Traffic

Admob, MoPub, Applovin, Unity DSP, etc. Lots of choice here.

Incent Traffic

Tapjoy, ironSource, FreeMyApps, NativeX, etc. Again, a lot of choice.

Programmatic Content Marketing / Native Ads

Taboola, Outbrain

Then you have a whole set of companies that offer managed out-of-home advertising / TV advertising and the associated measurement.

This isn't anything close to a comprehensive list, it's just a way of saying that there is a vast amount of choice out there beyond Facebook and Google.

Highly depend on your app. But  a very generic answer can be : 

• Games : test ad networks like Applovin / Unity
• non Games : you should consider ASA, Twitter, Pinterest and Snapchat and assess based on performance.