Don't be too afraid of higher ISO and the noise that comes with it. For one, when you can't get enough light down the lens, and can't use a slower shutter speed because it would produce an undesirable outcome (enhance camera shake, allow motion blur of objects moving in the scene, etc.), and using flash is not an option, then the only option left is to increase ISO.

Second, even if you have to push ISO to the limit, and end up with a fair bit of noise, removing a lot of that extra noise in post is not that difficult these days. Noise removal software is pretty advanced these days, and capable of removing or reducing a considerable amount of noise before doing so actually affects image quality enough that it actually matters.

If you just can't handle the noise, or you end up with complex forms of noise that are just plain difficult to deal with (i.e. electronic, color, and thermal noise artifacts of a considerable degree), you might want to invest in some additional lighting. You could try getting another, better and more capable flash, along with some gels for color correcting the light it puts out. You might also get a diffuser of some kind to soften the light produced by flash so that it doesn't create harsh and unsightly shadows. Getting a flash arm or simple tripod would also give you more control over how light falls and where it comes from, allowing you to dictate where shadows fall. The benefit of adding your own light to a dark scene is that you don't have to resort to any extreme measures when it comes to camera settings. You can use the aperture, shutter speed, and ISO that fit your needs, or are close enough to them, and not hassle with the problem in the first place.