How to properly format this date
I would suggest to already format entryDate within the group filter in the way you actually want to output it later.
To do that use Twig's date filter (→ see all possible formatting options).

{% set allEntries = craft.entries.section('tours').find() %}
{% set allEntriesByMonth = allEntries|group('entryDate|date("F")') %}

{% for month, entriesInMonth in allEntriesByMonth %}
    &lt;h2&gt;{{ month }}&lt;/h2&gt;

    {% for entry in entriesInMonth %}
        &lt;div&gt;{{ entry.entryDate|date('m.d.Y') }}&lt;/div&gt;
    {% endfor %}
{% endfor%}