The most notable thing about Gävle is that it is pretty much the only city that hasn't been conquered since Sweden became independent from Denmark in 1521. The archipelago protected us from the Russians, the Danes always focused on Stockholm and Norway wasn't a real nation so no one was able to get all the way up to Gävle.
The legal age for drinking in Sweden is 18 on pubs and 20 to buy alcohol at Systembolaget (the liqour monopoly) but most night clubs require you to be older in order to enter.
Things to see in Gävle
The railway museum, it is one of the best museums I've ever been to and I think that all information in the museum is translated to English (which is also true for most other museums in Sweden.
The prison museum
I have never been there but Nissedruva is a history nut so I guess we should trust him.
Vasaskolan, the number one senior high school in Gävle. Got a nice biology museum (not open during the summer).
Gävle got more sculptures per capita than any other Swedish city. Luckily it's funded by some kind of art foundation and not the city council.
The fifth element (30 000 €)
Valpen (30 000 € but the city council decided to sex up the rest of the roundabout at a cost of 100 000 €)
Gävle also got a nice archipelago and "Limöbåten" only costs 4€ to go with, I checked your profile and noticed that you like swimming so it might be a nice trip.
I think I have summed up pretty much all nice things about Gävle. I am born and raised in Gävle and it's not a terrible fun city to be in. Trains from Gävle to Uppsala and Stockholm cost roughly 14 € and take the same amount of time as going by car (or faster if going to central Stockholm). It might be worth visiting
this site if you got an interest in non-military history and got a car. There are many things to see within an hour of driving from Gävle due to it's historical importance in mining and the steel industry.
Falu koppargruva used to be the biggest copper mine in Europe and provided much of the funds necessary for Swedens rise to a great power in the 17th century. It is now open for tourism and have had famous visitors such as Osama bin Laden. Falun is the easternmost city of Dalarna which is a very beautiful part of Sweden so it might be worth it to go further west or at least visit some of the places where Gustav Vasa was hiding prior to his rebellion against the Danish king who ruled Sweden.
Sala silvergruva was the other major mine in Sweden and produced silver. I think it is more specatuclar than Falun due to the fact that you go down by stairs instead of an elevator. The surrounding area is also very nice, you can watch some movies about the mine
here.
Torsåker stollgång. It was far less important than Falu koppargruva and Sala silvergruva but it got some beautiful views due to the fact that it got several wide shafts leading down to mine that you can look up through.
Lövstabruk, one of the Vallonian steel mills established in the 17th century. Northern Uppland is a beautiful area and especially the mansions with surrounding steel mills from the 17th century are nice to visit.
Skokloster castle, it's abit far away from Gävle but an absolute must if you like military history due to it's nice collections. Also make sure that you visit the church, the interior is taken from the Polish monastery of Oliwa by Carl Gustaf Wrangel who built the castle and was one of king Gustav II Adolphus most important generals
There are of course also nice things to see/do in Uppsala (Swedens former capital) and Stockholm but they got webpages with collected information so I think it would be redundant for me to present them here.
Uppsala tourism and
Stockholm tourism. A common mistake is to underestimate the amount of interesting things to do in Uppsala and focus on Stockholm. In Uppsala you have
the cathedral which got a very nice treasury, the
university museum which is located in the oldest building of the oldest university of Scandinavia and old Uppsala
with it's viking museum.
In Stockholm I think the army museum, livrustkammaren (below the castle) and the Vasa museum are the most important to visit if your mostly interested in history.