Note on research when looking for new HQ

Research can be done at many NPC stations, or through the Mobile Laboratory and Advanced Mobile Laboratory POS structures. NPC factories generally have long queues for ME research, often as much as several weeks in popular high-sec systems, whereas PE research generally has no queues. As with manufacturing, there are cash costs for use of research slots at a NPC station. A Mobile Laboratory can do material research on three BPOs and time research on a further three at once, while an Advanced Mobile Laboratory can only do ME research on two at once and cannot do PE research at all. (Excerpt from EVE Wiki)