Pros
LLNL offers the freedom to do the research that you are interested in, IF you can secure the funding. Further benefits include a lax work schedule at a relatively high salary, with a decent retirement plan. Because of the size of the facility, there are experts in a variety of fields, so it is possible to have nearly any question answered. It all comes down to making connections and fighting through the internal barriers that exist, but if you are motivated and know what you would like to accomplish, it is a good place to get your research career off the ground.
Cons
The biggest drawbacks of working at the lab are the lack of bonuses or even non-monetary "kudos" for a job well done. Moreover, the facility seems to foster an environment of very poor communication; especially between management and employees. In this light, you must be a highly motivated self-starter in order to get anything done. Given the fact that LLNL is a government lab (or at least used to be) there is an ingrained slow-paced atmosphere with oodles of red tape to cut through. Be prepared to complete stacks of ridiculous paperwork and take weeks of near-worthless training courses before starting any project.