Is there any app that would allow me to preview the calendar from the menu bar (i.e. show calendar with a single click)?
It's all I need, I don't even need to open calendar from that app, though it would be nice.
A dedicated calendar menu bar item, Fantastical lets you view and modify your calendar from your menu bar.
Your events have never looked better
Plan your day in style with the most attractive calendar you've ever seen. Fantastical's beautiful design helps you quickly make sense of your schedule. You can even change the number of events you want displayed, allowing you to focus on what's important.
Need more info about an event? Just click on it and the event's important details will be displayed instantly.
Day-O is a simple menu bar clock replacement with a simple calendar for your Mac. It’s free, as-is (which means I’m not providing support, taking feature requests, addressing perceived inadequacies or releasing the source code).
You can do this with the Date menulet as part of iStat Menus.
Date & Time
A highly configurable date, time and calendar for your menubar, including fuzzy clock and moon phase. Open iStat Menus’ calendar to display upcoming events, or events for any day. Plus, a world clock with sunrise, sunset, moonrise and moonset times for over 20,000 cities.