Nobody will be offended.
It is a common practice among children to search for amber or shells.
However I would not expect too much.
Amber can be easily mistaken with other rocks and if you ever find something it would be rather of a small size.
The beaches along the whole coast are easily accessible and I can hardly believe in the existence of hot spots.
travel.stackexchange.com/users/1605/crenate
No, no one is going to be offended; In fact, it is a common practice, as already mentioned.
Random facts:
The best time is just after the storm, especially during winter.
I've heard some people go early in the morning for a search.
Never underestimate the place.
Sometimes you can find a lot of amber in crowded-looking part of beach.
There are even some guys who dedicate themselves to searching for amber and then selling it to tourists.
Similarly to those with metal detectors searching for lost goods at mediterranean beaches.
You will generally find rather small pieces.
travel.stackexchange.com/users/1758/Krizz
As I understand it, amber gets washed ashore and it is usually just little bits and pieces, probably nothing significant but a nice souvenir nonetheless.
Check Sopot beach .
It is mentioned at the site that it has some amber from time to time.
I believe you have the same chances of finding amber at any beach there.
travel.stackexchange.com/users/1593/rlab
Nobody will be offended if you look at a public beach and don't start digging large holes.
But be careful - after WW2, lots of unused ammunition was dumped into the Baltic, and sometimes fragments of phosphorous from incendiary bombs get washed ashore.
Those look very much like amber, except they spontaneously combust when they get dry and warm.
Quite a few people have suffered nasty burns because of this.
I'm not sure
whether that's a problem in the Gdansk area, but better be safe than sorry: if you find anything that looks like amber, put it into a bag, not your pocket, and don't leave it in your car unattended.
travel.stackexchange.com/users/1371/Michael Borgwardt
As was said earlier, it is recomended to search for amber right after the storm when you a lot of new stuff can be found at the beach.
But there are several special events - Amber Collecting World Championships
Here is a short video:
https://www.youtube.com/watch?v=xWwfODp64p4 Event dates for 2013: http://www.polawianiebursztynu.pl/artykul/53
travel.stackexchange.com/users/7174/Nick Kharchenko
I've read that one can find  amber  easily in the beaches in Gdansk. I believe it, but how to get to those beaches? Will anyone be offended if I go there and spend one hour looking for amber?
Where can I go looking for amber in Gdańsk, Poland?
travel.stackexchange.com
<beaches><activities><poland><gdansk>
travel.stackexchange.com/questions/5380
travel.stackexchange.com/users/1425/Ivan
Nobody will get offended, and it is a common practice among children to search for amber or shells. Sopot Beach is a good place to look, and it is recommended to go early in the morning and especially after a winter storm. You can sometimes find a lot of amber in crowded-looking areas of beach, but the pieces are usually small. Looking for amber on the beaches around Gdansk is a common practice and everyone is free to do it, although, in general only small pieces are found. The best time to search is said to be after a storm and also, perhaps, in the early morning. 
Looking for amber on the beaches around Gdansk is a common ractice and nobody will be offebded if you do it. The best times to look are after a storm and maybe also in the early morning. Generally the pieces are small and found everywhere, even crowded beaches. Sopot beacj is recommended.