I'm not sure where you are located, so I don't know what you consider local.
Here in Ft. Wayne I have had work done at a few different shops.
Modern Primitive (no longer around)
Artisan Tattoo
New Republic
Pixel & Pigments
Studio 13
I have yet to find a 24 hour shop in Indiana.
Don't go somewhere because it is cheap! Go to an artist with good rep and be willing to pay for his skills. Otherwise, you can get a "bargain" and end up with a bargain tattoo for life. Save money up and get it done right.