There are some standards from Fiddler on the roof and also Mary Poppins which some might like to hear. I was going to suggest some of the same things Ron did. Here are a few I remember my mom and dad playing:

Sentimental Journey
Tennessee Waltz
Missouri Waltz
Waltzing Matilda
I'll take you home again, Kathleen (they did that for me as that is my name:-)
When its springtime in the Rockies

and scads more I cannot remember

Blue moon is one I played in a quartet as well as Moon River

I'll look at my set list and post a few more, tomorrow.