We were thinking of stopping in Gorlitz on the way from Dresden to Berlin (we will have a car). How easy is it to park near the border and walk across the bridge for non-EU visitors?
Shouldn't be any problem at all. Poland officially joined the EU in 2004, and joined the Schengen area (meaning no border controls) a year ago.
In June 2008 we were able to walk across the pedestrian bridge that used to be only for EU citizens.
It's as easy as crossing a bridge from GA into FL or any other neighboring state. There is no real border, on the pedestrian bridge there isn't even a mark on the pavement or so. BUT why would you want to go to the Polish side of Görlitz? Form the German side you can already see that there really isn't anything to see on the Polish side - other than cheaper gas stations and a bit lower prices in supermarkets. A half-day trip much more worthwhile from Görlitz is to visit the old town of Zittau, about an hour's drive (actually less) from Görlitz. If you want to drive through two worlds in one afternoon do one drive Görlitz-Zittau on the German side and the other (Zgozelec-Sieniawka) on the Polish one. While the German side is 21th century on the Polish one the villages look like early 20th century and you can even sometimes see chicken and geese walking in the main streets. Also watch where the bus stops of those Polish villages are ;-)... From Zittau take the former border crossing in Chopin street. Right after you've crossed the river you can follow signs to Zgorzelec. You can find that border crossing within Zittau (a small town) by following signs to Reichenau, which is the former German name of Bogatynia, the next larger town on the now Polish side of the Neiße river. I've just been to the area over New Years so if you have any other question feel free to ask me. Oh, and one more thing: Polish gas stations right behind the border are more expensive than those further away from the border. BUT the closer ones show prices in € per Liter just as they do in Germany whereas the other, real Polish ones, show prices in Zloties per cubic decimeter. Zittau itself is in the three-countries corner of Germany, Poland and Czech Republic but filling up in Czech is as expensive as it is in Germany - so only Poland really is interesting in that regard.
However, there is a castle on the Czech side of Zittau called Burg Grabstein (English: Gravestone Castle) which really is worth seeing - even if just from the outside. To get there from Zittau follow signs to Liberec/Reichenberg. Grabstein is a village en route about 15mins from downtown Zittau. From there return towards Bogatynia and further on to Zgorzelec.