A solid follow up to Bad Beginning, The Reptile Room follows the Beaudelaire children to a new home, and to new horrors. 
 The jokes and tone are very consistent with the first, so people who didn't enjoy Bad Beginning really shouldn't bother. As it was, we liked it quite a bit. My kid loves the titillation of the horror (which is only just barely stylistic enough to qualify as "for kids"), while I'm enjoying the dark humour in the narrative style. 
 I love that the series explicitly uses - and even explains - literary techniques. Just as an example, there's some dramatic irony in Reptile Room that the narrator actually names and explains. It's such a wonderful way to introduce my youngling to concepts, not to mention to some bigger vocabulary. Plus, "herpetology" is terribly fun to say.