I started my journey to Sag A last week, probably on Thursday or Friday. I try to go about 1k light years a day, but will sometimes get 2 done if I have the time. I'm currently about 18k from Sag A. I've traveled outside our home arm of the Galaxy and crossed the next one, I'm about to enter another arm. I went by way of the Lagoon and Trifid nebula's for a bit of sight seeing on the side, but decided in the end that nebula's are fun for finding odd stars, but decided to focus mostly on the prize at the end and have stopped site seeing.
So far I've found 3 earthlikes, several water worlds that I mistook for earthlikes, one black hole (who's location shall remain secret as I have a discovery in that system I want to cash in), and lots of strange system with interesting configurations.
My current process is to jump in, hit the scanner. If the star is scoopable, I get close enough to pull 80 to 120 per sec from the star, stop and start scanning it while I pull up the system map. If I see anything unusual, I go scan it. If not, I leave as soon as the scan stops.
When plotting my course, I usually look for a blue star to end on because I've noted they tend to be larger and thus have more interesting solar systems.
I probably won't be at Sag A until the end of this week or early next week.
EDIT - so far I've only had one "Stall" where my computer didn't load the star textures right away and I ended up getting pulled out of supercruise. the heat sink saved me from getting anymore than just minor damage.