Personally, I'm more like that first type. I quest hard until top level, then take a break from it while I work on other things. I quested through Storm Peaks in the Wrath beta, but I haven't done it on live yet. I hit level 80 in Icecrown and haven't done much questing since then, I've mostly been running raids and heroics, finally replacing my level 70 gear. My first goal, though? I wanted the Reins of the Red Drake.
Since long before even The Burning Crusade introduced flying mounts, I wanted a red dragon mount. I don't really know why I wanted it, but I did. When I saw that you could get the drake in Wrath of the Lich King, I had to have it. Yesterday, I hit Exalted with Wyrmrest Accord and spent a good hour flying around Northrend on my new mount. Argent Crusade is probably the next rep I'll work on for the Argent Champion title.
What about you guys, what's the first thing you worked on at level 80? If you're not 80 yet, what do you plan on doing first? Are you after something specific, or are you just going to keep on truckin' with your questing? Any achievements you have your eyes on?