/me/associated is the preferred way to turn an access_token into a list of users, it returns the collection of per-site user details that can be quickly fetched. It's basically the user's account tab.
If you need more details about a user on a give site, then turn around and hit /me (or /users/{ids}) on the sites you've discovered via /me/associated.
As for display names and profile images, you will have to make at least one call to a site specific method; I typically advise consumers to only query the user's top account (by rep) for that information, it's the same on all sites for > 90% of users with multiple accounts (and > 50% of users only have accounts on a single site). However, if you intend to display all of a user's accounts you will have to make multiple requests.