The best part of a visit to Goslar is exploring the narrow winding side streets. Keep exploring, you don't have to worry about getting lost. Signposts for pedestrians have been put up everywhere. They point the way to the different sights and will help you to find your way.
Getting to Goslar is no big deal without a car. Regional trains hit Goslar both on the lines from Hannover/Hildesheim to Halle along the Harz mountains, from Göttingen/Kreiensen and from Braunschweig. The RE line Hildesheim-Halle also runs through Bad Harzburg, Wernigerode, Halberstadt, Quedlinburg so the most interesting places to see along the northern foot of the mountains can easily be reached.
Up into the mountains, however, you'll need buses because there are no train lines in the western part of the Harz.
The train station is situated on the edge of the old town (blue flag on the map in photo 2). From here the town centre can easily be explored on foot. To the market square it's about 10 minutes walk.
There are good roads but if you have no car, then catch a train to Braunschweig and change there. It doesn't take too long and you pass Germany's oldest railway station on the way, then the mountains appear in the distance and sort of pull you in like a Death Star but nice :-)))