G12 Shooting from a dark area to a lit one?

What would be my best setting without a flash? I was using P mode in this shot and it isn't bad but is a bit overexposed due to the lights.

Any other options to get better clarity without becoming grainy?

In scenes such as this one it is very difficult to obtain detail in both the dark and light areas. Typically, a decision is made to either give up the dark or light area detail. In particular, it is probably advisable to give up the details around the bright light. This fine tuning can be done by using exposure compensation to get the desired effect or by using Manual exposure mode.

By shooting in RAW mode and doing some extensive post processing, an image can often be tweaked to show more shadow detail and less highlight clipping.

Yet another option is to shoot, say, three shots and combine them using High Dynamic Range (HDR)techniques and software.

^ What Gordon said.

For the exposure bracketing though, it's advisable to use a tripod so it's easier to line up the exposures. You can do this by using the HDR scene mode or using AV and turning on exposure bracketing and using software to combine the photos (the latest DPP, Photomatix, etc.)