Line breaks in textarea element

You can use <div> with contenteditable attribute:

<div contenteditable="true" style="width: 450px; height: 300px; white-space: pre-line;" name="familyPlanningClinicSessionsClinicTimes">Monday:
                            Tuesday:
                            Wednesday:
                            Thursday:
                            Friday:
                            Saturday:
                            Sunday:</div>

But in your case I think idea solution will be just using several ordinary text boxes, one for each day:

Monday: <input type="text" name="familyPlanningClinicSessionsClinicTimesMonday" /><br />
Tuesday: <input type="text" name="familyPlanningClinicSessionsClinicTimesTuesday" /><br />
...

You could use the 
 (it means new line in html) but maybe that's not a nice formatting, like you said...

The only way I can think to remove this issue is to remove the indentation. Its not the end of the world, but is there another way, to keep the nice formatting?

<tr>
  <td class="label">Clinic Times:</td>
  <td><textarea name="familyPlanningClinicSessionsClinicTimes">Monday:&#10;Tuesday:&#10;Wednesday:&#10;Thursday:&#10;Friday:&#10;Saturday:&#10;Sunday:</textarea></td>
</tr>

There isn't a pure HTML solution to your problem. Textareas always display any whitespace in their contents.

In a perfect world, you'd be able to take advantage of the CSS property white-space; unfortunately, it isn't applied to textareas either.