Swedish Railway Museum.
One of the world’s finest collections of locomotives and carriages, together with facts and articles from Sweden’s railway history, are on display at the museum. Different exhibitions and activities are organised during the year. Open throughout the year. Closed on Mondays in the winter.
Every year, in the beginning of august (this year between 4th-7th of august), the kernel of the city turn into a swarming festival. You can choose to walk around looking at the market stalls, try food from the whole world or just listening to the artists. The festival is for free.
Have a visit to Högbo Bruk. You will find Högbo bruk, just north of Sandviken, a city west of Gävle.
For more photos, please have a look at the Högbo Bruk travelogue.
Since Gývle is home to the Swedish Ordnance Survey, there are lots of things related to mapping and geography here (maybe that's why I like it). You can visit the mapping centre (office hours only) with aereal pictures, old maps of Sweden, info on new mapping techniques and a research archive.
Mackmyra Swedish Whisky was established in 1999 as the first Scandinavian malt whisky distillery. The whisky is not yet for sale but will be a single malt, with a unique Nordic character. Mackmyra is the only distillery in Sweden, thus adding a new dimension to the national tradition of vodka and aqvavit. The distillery is situated 10 kilometres west of the city of Gävle and 200 kilometres north of Stockholm, which makes it the nothernmost distillery in the world.