Depends on the audience I guess. What kind of people frequent this bar?
Generic advice: Being a bar, kick off with a technically tricky or ironic song to win them over, as their initial - possibly drunk - impression about ukes may be against you. You've got to catch their attention early on. Check out songs by
The Reentrants for ideas.
Then a couple of your own songs, or songs they might not expect (pop, rock or comedy songs from the last 20 years), or songs you have in your repertoire that are secret gems. The type of song where they come up to you afterwards and ask you what it's called. Or just play
Freebird.
Then finish up with a couple of crowd participation songs such as yelling "Faster" for the Crazy G, or a few sing-a-long songs.
And keep the feel of the songs positive and upbeat - just like the uke. The last thing you want is to rock a set where everyone is happy and buying drinks (something that Bar owners will like, and may ask you to come back again) only to play something depressing or downbeat like Fake Plastic Trees. The last thing you want in your life-long ukeventure is a bar full of drunken emos.
Maybe throw in a bit of banter between songs - keep it brief, maybe factoids about the uke ("did you know about its Portugese heritage? blah blah")
I hope that wasn't too generic, have fun, good luck, and let us know how it goes! Or better yet, get a friend to record it. You can watch it later and see for yourself any areas that you might be able to improve!