So CCP release static data that contains all kinds of information that the game uses. This includes full details of all of the systems in the game.
Based on the current static data, in terms of space that anyone can visit:
| Region Type | Solar Systems | Planets | Moons | Asteroid Belts | Stargates |
|---|---|---|---|---|---|
| Highsec | 1,192 | 10,233 | 50,910 | 11,951 | 3,431 |
| Lowsec | 688 | 5,832 | 29,674 | 7,144 | 1,837 |
| Nullsec | 3,321 | 28,130 | 144,495 | 21,831 | 8,464 |
| Wormholes | 2,604 | 21,789 | 107,519 | 0 | 0 |
| 7,805 | 65,984 | 332,598 | 40,928 | 13,732 |
Of note there, wormholes have no gates. You access them by scanning down signatures in space, warping to them and then passing through the wormhole into the wormhole systems.
So you’ll need scanning skills to be able to explore wormholes.
In addition, there are 3 Regions of space that are not generally accessible. These are thought to be inhabited by the Jove Empire and they turned off all of the gates.
As a result, in addition to the 7,805 systems that we all can explore, there are 230 additional systems we can’t reach, with (1,977 planets, 9,572 moons, 0 asteroid belts, 32 gates).
There is a possibility to reach 2 of those systems, but only if you take part in an Alliance Tournament (annual esports tournament, which uses 2 Jove systems for the fights).
In addition, there are a lot of monuments to visit around the place. So are part of New Eden like the EVE Gate, where the first wormhole came to; and others are monuments to player activity (eg. Titan graveyards at/near the sites of major battles).
I don’t have a detailed list of all of the places to explore, but you could start here:
Good luck.