The option offered by techraf is one way to go, but I do think there is a built-in OS X option available that will meet your needs (or most of them).
In every OS X 'Open' dialogue box or 'Save as' dialogue box you have a drop-down menu which you can click on to select other locations. Clicking on this will also list your recent places and allows you to open from or save to these as needed.
Depending on your setup, you may need to click on the arrow button appearing next to the field (on the right) to make the drop-down visible.
As an aside (and you're probably aware of this - but for the benefit of others) on a related note you can access recent applications and documents under Apple Menu > Recent Items.
You can also increase/decrease the number of recent items listed here by accessing System Preferences > Appearance on older systems or System Preferences > General on newer ones.
Hope this helps.
Okay, here are some images showing an example of how to view recent places in Mac OS X Save As dialogue boxes and Open dialogue boxes. These examples are based on OS X El Capitan, but other versions also work in a similar fashion.
- Various applications may display these dialogue boxes differently, but all offer the ability to view recent places
- In my images, Desktop is shown in the Where drop-down menu. However, this may be different depending on your circumstances
- If you can't seem to see a list of recent places, make sure if there is an arrow next to the Save As field that it faces down (see below)
Hope this helps!