stigcq

A plugin offering a widget showing recent photos in posts. It can be configured 
as for how many photos to show, the title on the widget and max width and height for 
thumbnails.
The thumbnails links to the post where the photo is showing. They show a mouse over 
effect with bigger version of the photo in a tooptip.
It has option to exclude photos from the view.
It has only been tested with WP 4.2, it might work with lower versions.

Recent photos widget

A simple widget which shows thumbnails of latest photos in posts

lyrathemes

Social Images Widget is a no fuss, simple to use WordPress widget to display your latest Instagram photos.
Due to the changes in the way the Instagram API can be utilized, this widget can only be used to display your own own profile info and media. Inspired by the simplicity of the WP Instagram Widget (which is no longer maintained), this plugin uses sensible and simple markup, and provides no styles/css – it is up to you to style the widget to your theme and taste.
<a href="https://help.lyrathemes.com/collection/364-instagram-widget" rel="nofollow ugc">Documentation</a>
<h3>Setup / Instagram Authentication</h3>
This plugin requires that you authenticate your Instagram account. In order to do so:
<ul>
<li>We will redirect your request to the Instagram authorization URL. </li>
<li>If the you are not logged in to Instagram, you will be asked to log in.</li>
<li>You will then be asked if you would like to grant our Instagram application “LyraThemes Social Images Widget” access to your Instagram data.</li>
<li>Our application simply facilitates your access to the Instagram API, so you can use our plugin to access your Instagram feed. Please note, while your access data gets routed through our website at https://www.lyrathemes.com, it does not get stored at all in any form and is a simply a means to move the authentication data back to your own website.</li>
</ul>
<a href="https://developers.facebook.com/docs/instagram-basic-display-api" rel="nofollow ugc">Instagram Basic Display API</a> 
<a href="https://www.instagram.com/about/legal/terms/api/" rel="nofollow ugc">Instagram Platform Policy / Terms of Use</a>

Social Images Widget

Social Images Widget is a no fuss, simple to use WordPress widget to display your latest Instagram photos.

Recent photos widget vs Social Images Widget