I think a Thursday night would be great.
It's near the weekend, but not quite the weekend, & you'd be surprised how many people go out on weekdays, especially if they work weekends.
Plus, the band would probably be cheaper on a week night.
Do you have student nights in your town? Where I live (Wales, UK), we have student nights, & most bars & restaurants do special offers for them. If you have this sort of thing in your town, get the live band in for that night.
Advertise it for free on facebook, & I'm sure you'd draw in a good crowd.
Offer 2-4-1 cocktails too!