How to display javascript console on Chrome (or a different browser)? I want to quickly try some Javascript code on Android phone. 

I cannot find how to open console or something similar on either Chrome or default browser. about:debug doesn't do anything, and I don't want "remote debugging". 

I can download another app if necessary (but I don't want to root my device).
That feature seems to be unavailable for all major android browsers.
You could try Opera-mini instead:

Reset the console output by opening a new tab with the address debug:resetconsole

Open a tab on the page on which you want to do the inspection:

Run JavaScript code on the page by replacing the address in the address bar with the following address javascript:var%20n%3Ddocument.firstChild%3Bwhile%28n%20%26%26%20n.nodeType%21%3DNode.ELEMENT_NODE%29%20n%3Dn.nextSibling%3Bconsole.log%28n.outerHTML%29%3B
Retrieve the output by opening a new tab with the address debug:console