I plugged in a few numbers, and came up with the following escape velocities:

- Earth, from the surface: 11 km/sec

- Earth, from geosynchronous orbit: 4.7 km/sec

- The Sun, from Surface: 617 km/sec

- The Sun, from Earth's distance: 42 km/sec

Note that if you take off in the direction of rotation, the rotational speed of the planet subtracts from the speed which must be reached by the rocket.

So, for example, the Earth's equator rotates at 0.5 km/s, which is a useful discount from 11km/s.

For more, see:

https://en.wikipedia.org/wiki/Escape_velocity#List_of_escape_velocitiesSince it is difficult to get a rocket that can accelerate an object to 42km/s to escape the Sun, so a gravitational slingshot past the Earth and Jupiter can give it an extra velocity kick to escape the Solar System.

It's not so easy to calculate the escape velocity for a distributed object like a galaxy (or a galaxy cluster). The approach is to plug in the total mass of the galaxy which lies inside the Sun's orbit around the galaxy (including the invisible Dark Matter), and the Sun's distance from the center of the galaxy.