I've been using Google Calendar, but it displays events from both of my calendars together, just with different label colors for the events. I'm looking for a way (not necessarily with Google) to have a single account that will let me create any number of completely separate calendars, with events that do not commingle. I also need the ability to display one of the calendars in a European time zone, so U.S.-only solutions will not work.
Google Calendar can have different clanedars with different time zones. In the left menu where it says "My Calendars" click the little dropwdown arrow and click "Calendar settings". You'll be taken to a page dedicated to settings for that calendar and near the middle of the page is "Calendar Time Zone."
There you can change the time zone for that one particular calendar, and it will stay separate from other calendars.
To display ONLY that calendar, click the little dropdown arrow and click "Display only this calendar."
I just tested it and it worked perfectly :)