What is the best place to grind experience?

I like to fight the dinosaurs in the "dinosaur shaped forest" in the World of Ruin when I'm trying to level my characters. This forest is located on an island in the northeastern part of the map, just west of Triangle Island. I believe Brachiosaurs and Tyrannosaurs spawn here.

If you know Vanish and X-Zone, and have the Gem Box (aka Soul of Thamasa), you can double-cast these two spells on them to kill them instantly. The GBA version closes this loophole, but I don't know which version you're playing. Brachiosaurs frequently drop Economizers (aka Celestriads), and you can sometimes steal Ribbons from them, which is an extra boon.

If you're trying to level your whole party, you can leave one high-level magic user in while you gain levels on the others, so that you can power level the rest of the active team. The Brachiosaur casts very high level magic very quickly, so having appropriate speed enhancing relics is also a plus.

If you're not high enough level for this forest yet, you might try the Veldt, which has the advantage of teaching Gau new abilities if you have him in your party and Leap when you encounter something new.

Along with XP grinding, there is the question of MP grinding. The answer to that is the desert area just south of Maranda. Hoovers are high on HP, but I've found using Offering + a weapon with a instant kill chance CAN end the fight quickly, before he starts using "Crush" to instant kill your toons. 5MP per hoover isn't bad and the XP is pretty good as well.

Also located there are the Cactuars, worth 10MP / kill, but no XP. For an easy time with them, equip the Atma Weapon and give them Sniper Sight relic. The 100% hit rate ensures the hit, and the Atma Weapon does damage based on your character's HP, ignoring all defenses, just like Edgar and his drill, IF he actually hits with the drill. Since Sniper Sight only applies to "fight" command, this combo of weapon and relic guarantees a one shot kill on the little buggers, putting 10 Magic Points in your pocket, along with 10k gold no matter who you put them on. So if you need to learn spells quickly from espers, this method will do the trick. After ten cactuar kills, just avoid the center tile on the lover left portion of the desert, so you don't run into the Gigantuar...unless you're ready for him!