Anything, even neutronium, that would gravitationally attract you at 1G would have the mass of the earth.
Not true; since distance also plays a role in the force we don't need and Earth size mass to feel an Earth sized acceleration. With a compact mass equal to Everest such that we could stay 35 meters from it's center we'd feel a 1g force. At 10.25 meters We'd get 11g. We accelerate that at 10g and live in the nadir 1g point. The tidal forces would likely be a bit uncomfortable if we're much bigger than a soccer ball, but we can't have everything, now; can we?
It's not the man that knows the most that has the most to say.
Anon