There are 10 Wild Artefacts in the game, and 10 gates to open with them. If you want to open all of the optional areas, you must buy the Wild Artefact from Serendipity.
There are 7 Graviton Cores and you need 5 to progress the game. Cores can be found in the following places:
New Bodhum 003 Bresha Ruins 005 Oerba 200 Academia 400 Yaschas Massif 100 Oerba 400 Sunleth Waterscape 400
Note that Yaschas Massif 100 AF contains both a Wild Artefact and the gate to Sunleth Waterscape 400 AF, and Oerba 400 AF requires two Wild Artefacts to access.
There are 7 Wild Artefacts available up to this point, plus the 8th in YM 100, and a 9th in Serendipity (the 10th isn't available until later in the story). Not counting the gates to YM 100 and Oerba 400, there are 6 gates that can be opened with Wild Artefacts.
Therefore, if you've found all of the "free" Wild Artefacts, you can always access at least 5 Graviton Cores without purchasing the one from Serendipity. Accessing all 7 of the Graviton Cores might require a purchase, depending on which other gates you've opened.
The other 3 are in times where I don't have access to :/ Had a wild artifact, but I think I messed up and used it on Vile Peaks which just seems to be a random sidequest area, so now I struck with no other free wild artifacts to open up at least one place to go to.
Hentai = Art "Its all about love, friendship and courage! - Laguna, FF8
There are (or were) Wild Artefacts in the following locations:
Bresha Ruins 005 Bresha Ruins 300 Oerba 200 Sunleth Waterscape 300 Archylte Steppe ??? Augusta Tower 200 Academia 4XX
If you have not opened up Yaschas Massif 100 or Oerba 400, then you could have potentially opened all of these gates: Bresha Ruins 300 Yaschas Massif 110 Augusta Tower 300 Vile Peaks 200 Oerba 300 Vile Peaks 010
That's 6 gates and 7 Wild Artefacts. At least one is unaccounted for.