At the center, the sky would be bathed with a diffuse light probably as bright as the Full Moon in some directions. There would be thousands of red stars all over the sky, each one probably as bright as Venus. There might be a few directions where, looking out of the nuclear disk, you could see into parts of the rest of the Milky Way, and looking straight up, out of this disk, you might see a few bright galaxies, but the dust and gas emissions would make cosmology quite hard.
At the 'rim' of the Milky Way, looking away from the center of the galaxy in the opposite direction, the entire hemisphere...or more...would contain almost no stars, but you would see faint spots here and there that are the distant galaxies. Looking into the galaxy in the other hemisphere, you would see a thin disk of light produced by the stars in the Milky Way, just like you see in our night sky, but the band would be narrower and fainter, and there would be very few bright stars in the sky that are very far above or below this disk. That's because the brightest stars we see around us here are distant giant stars in the disk of the Milky Way. From a vantage point near the rim, these stars would be crowded into a band not much thicker than the faint Milky Way itself.