As with catcher and first base, deciding who was the best Mets' second baseman of the aughts wasn't much of a challenge. Edgardo Alfonzo was only with the Mets for three seasons this decade but he was still more than thrice as valuable as the next-closest entrant. Alfonzo was a five-plus win player four times with the Mets, including a career best 7.0 WAR in 1997. Originally a shortstop in the Mets' minors, Alfonzo was moved to third base because Rey Ordonez was deemed the better player of the two. Fonzie played parts of four seasons at third with the Mets before their signing of Robin Ventura forced him to second base, where he played for four seasons, three of them of the five-plus win variety.
The runner up on this list is Jose Valentin, who was an afterthought when Omar Minaya signed him prior to the 2006 season. His $912,500 contract was considered such a colossal waste that a blog popped up to lampoon that very fact. Valentin surprised everyone by posting a three-win season in 2006, earning himself a raise for 2007, during which he was basically a replacement-level player.
Luis Castillo we all know. Not good, not bad.
Damion Easley was like a 2007's lesser version of Jose Valentin. Easley was signed to be a decent right-handed bat off the bench, but he got almost 200 plate appearances and was better than 1-WAR. He came back in 2008 and was mostly worthless.
Roberto Alomar was acquired in a blockbuster trade with the Indians in which the Mets sent top prospect Alex Escobar, Matt Lawton, and Billy Traber, among others to Cleveland. Alomar was coming off an 8-win season in 2001, a 5-win season in 2000 and another 8-win season in 1999. He was going to be 34 in 2002, but few could have predicted the shocking and abrupt cessation of all usefulness as a ballplayer that Alomar experienced as soon as he put on a Mets' uniform. He was, in aggregate, a replacement-level second baseman over the final three years of his career, from 2002-2004. He's still a hall-of-famer, but don't ever expect to see his mug prominently displayed at Citi Field.