How to use multiple google accounts, but allow only one to locate my phone in device manager
By going to the sync settings for each account (as shown in the image below), you can control what each account 'sees'. For the 'public' account, turn off all syncing besides Gmail and Calendar.

Unfortunately, this will not address Android Device Manager access. To do this, you must open the Google Settings app and navigate to Google > Security. Below Android Device Manager heading, you will be able to turn off it's features.
Source: Set up Android Device Manager

(Click image to enlarge)