[Pseudoscience-is-malarkey (OP)]

There's an escape velocity to escape a planet, a star and a black hole. Is there an escape velocity to escape our solar system? Our galaxy? Our Local Group?

[CPT ArkAngel]

Yes, but it depends where you start, the time and the direction you want to go. All matter is affecting you and all matter is moving.

[Bored chemist]

Yes, there's an escape velocity for any massive object.
One way to calculate it is to imagine a distant object falling in towards the solar system (or whatever).
As it "falls" towards iu it picks up speed. When it reaches us, it's at the escape velocity.

[evan_au]

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_velocities

Since 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.