Well, in my opinion its not a grindy game. There are aspects which are grindy, but the beauty of eve is that you dont actually have to take part in those areas if you dont want to. An example is mining. I've gone my whole Eve career without mining a single piece of ore.
Unlike most other MMORPG's where there is a clearly defined 'endgame' and clearly designed progression, EvE puts it squarely in the hands of the player. Apart from some NPC controlled high security areas, all the territory is owned by rival factions, and the economy, barring shuttles, is completely player driven.
And grinding missions? eurgh. Eve's beauty, in my opinion, is in its PvP system. Its not just killing the other guy, its taking over his space, destroying his stations and basically waging all out war on him!
That and there are ships with lasers which actually go 'pew pew'.