In Jantarnoje town there is a museum of amber (when you arrive in the town by car by the main road you'll directly see the indicator to go to this museum) where you can see some history of extraction of amber in those places and even some soviet heritage.
Also you'd love to buy different original jewellery with amber that is presented here with wide range of it: rings, earrings, bracelets, collars, various sets from them (set prices are from 1000 Rub). The prices for single jewellery are from 120 Rub and up.
Outdoors in the streets of Svetlogorsk one will definitely find the Salesmen / women behind their stalls selling the Gold Of the Baltics.
What to buy: Necklaces, other jewelery made (partly) of Yantar = amber
What to pay: not too much...at least for a necklace not more than €25.00 otherwise one better go to an official Point of Sale