What is the range of the Starkiller Base in The Force Awakens?

Question

Since the Starkiller Base is a huge planet, you would think it would be pretty hard to move to get closer to other planets, and it would also need to travel to other stars to actually refuel. But we see in the film that they fire the weapon in what seems like pretty quick succession (say, a few days at least).

The first time was at the Republic, and the second time at the resistance.

Either

1. the republic base and the resistance base were very close together and there were just more than one star around the base

2. it has the largest rockets in the universe to move it

3. it has a HUGE range.

Which one of these is it, and if it's #3, what's its range?

Answer 1

It's #3. And the range is exactly "half the galaxy"

From the Foster novelization:

Finn nodded. “General Hux told us it’s the most powerful weapon ever built. He said that it can reach halfway across the galaxy.” Fresh murmurs of disbelief greeted this latest assertion. “And in real time. Because it doesn’t reach across the galaxy; it reaches through it.” He shook his head, which was starting to hurt from the effort of trying to explain what he had overheard but did not understand.

And the exact way the weapon works is described in this asnwer.

Answer 2

Being its system's star the source of energy for Starkiller Base, it wouldn't be possible (or practical) to move the Base. In fact, Starkiller Base doesn't need to be close to the planets the First Order intends to destroy. As we read from the official site's page on the Base for Star Wars:

Starkiller Base

Deep in the Unknown Regions, the First Order has constructed a superweapon that uses an entire planet as its weapons platform. The deadly Starkiller harvests energy from its system’s star, contains it within magnetic fields inside its base’s planetary core, and then converts that energy into an ultra-powerful beam that blasts through hyperspace, able to sterilize the worlds of a distant star system with a single shot. The icy world that houses the Starkiller is the First Order’s greatest secret, and essential to its plan to conquer the galaxy.

So the fact that the beam produced by the Base can travel through hyperspace makes the range very huge. Indeed any known hyperspace route can at this point be used to reach the target the First Order intends to hit.