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What is the average distance between stars?

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That all depends. The core suns are packed fairly tight, about 1/4 light year apart. Out here closer to the rim the stars are spread out some 5 to 10 light years apart, for solitary stars like our sun that are not part of a cluster. The stars in the Pleiades form a tight little knot, fractions of a light year apart, as they do in the Orion Nebula.

We could do a little math. The galaxy is lens shaped, about 10,000 light years thick at the center, but 3000 light years thick out by us. The diameter is some 100,000 light years across, and the core not much more than 10,000 light years. Since 90% of the galaxy is 3000 light years thick or less, we'll just represent the galaxy as a cylinder with a 50,000 light year radius and a height of 3,000 light years. That gives us a volume of 23 trillion light years.

Now there are 200 to 400 billion stars distributed through that volume. If we take the average, 300 billion, the ratio gives us the average volume surrounding each star. 23 trillion divided by 300 billion is 78 cubic light years per star. The cubed root of 78 is about 4.3 light years. This corresponds fairly well to the published figure of 3.5 light years. (I posted this question on an astronomy club mailing list, and one of the members wrote back).

If you include the distance between galaxies, the average distance between stars expands significantly. I just assumed you wanted the average for the stars within our own galaxy.

Personal travel between star systems is unlikely, unless some kind of tunnel (wormhole, Nexus bridge, tri-dimensional rapid position shift--TDRPS, or some other speculated shortcut) is discovered with distinct destination points, with the possibility of returning to the origin point, the consideration is wholly moot beyond the ramifications of gaining more precise knowledge regarding astronomical distances for improved comprehension as a matter of course. Even considering cryo-suspension for tremendous periods of time, as the time shift would ensure that no return trip could have relevance for hundreds of generations. For foreseeable decades our focus must pertain to the gradual exploration of our own solar system, and it will be a slow process.
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