I absolutely love the research. Maybe it's the academic in me but more likely it's the excuse to pack a bag and take off for new places. I wrote a short crime story while sitting outside a cafe in the Place de Concorde, Paris, and I was arrested on Mallorca while researching my Hot Air novel - haha. Really! For my medical mystery / scifi novel ARIA: Left Luggage I spent a year on research before settling to write the novel properly. Partly it was because the original premise of infectious amnesia demanded that I knew some memory-related neurology as well as location geography. Don't get me started on how I love research. Ah, too late.
Each project is different for me. I've done similar to you on some stories, but others I've done all the research up front before even starting the outline. I wish there was a reason for it, but there isn't.
Occassionally I'll do some research while I'm writing the first draft, or before starting a first draft, but the majority of the time, my research happens in the 2nd draft. I feel doing research hinders my creative flow when I'm writing the 1st draft. I'd rather be completely wrong in the first draft than to stop everything to seek an answer and then have to spend time to get back into the flow of things.