How do you expect a potential customer to recognize you and your tweets in a crowded sea like this?
In this case I think it is clear that the default Twitter avatar is not ideal. it is also worth noting that a transparent background for your avatar is also not ideal as many Twitter users are viewing their feed and tweeting outside of Twitter.com.
Exterior shots, of hotels in this case, are very small and while the hotel might recognize the location it will be difficult for customers to identify the image.
Use of the brand logo appears to be a good option if you have one that will work. Hilton Garden Inn has an easily recognized flower with the red background. Consistency from a brand would be key when a franchise is involved like in this example.
It is important to remember that people are not waiting for a message from you via an Inbox. They are scanning lines and lines of messages from many different sources. Make sure people can easily pick you out.