Where is the best place to level up in Final Fantasy X

Here's a list of all permanently missable items in the game.

• a no encounter weapon, as an equipment drop from Geosgaeno.
• a magic counter buckler, from the hovercraft merchant in the Calm Lands.
• the 0-Slotted Longsword can't be bought after a certain point.
• Master Spheres are limited in quantity.
• the four Al Bhed Primers from 19 till 22 are (technically) missable.

Also, certain non-items are also permanantly missable.

• Having Wantz in Macalania Woods selling 4 slot equipment
• You can't recruit Durren for your Blitz team anymore after a certain point.

For more information, there is a FAQ on GameFAQs giving detailed information for all of these items

According to this article,

you have to capture 10 of EVERY fiend in the entire game... then you have to beat all of the Area Conquest, Species Conquest and Original monsters in the arena.

Also provided are preparation tactics:

you MUST have weapons that have Break Damage Limit and One MP Cost, armor with Auto- Phoenix and Auto-Haste would be nice too. Have the person/people with One MP Cost know Auto Life so the others do not have to waste precious MP casting it. Quick Attack is also helpful.