I have done Uber a few times in Sweden and it worked well. Unlike in London, it is not cheaper than a regular taxi but the price difference compared to normal taxis is small. Unlike in London, it is very easy to prebook with a regular city wide taxi company like Taxi Stockholm or Taxi 020. Unlike in NYC, Uber cars in Stockholm are not fancier than regular taxis.
The main advantage with Uber in Stockholm is that you don't have to worry about getting ripped off by an independent driver. But don't use Uber to/from Arlanda airport, the fixed prices most regular companies use are lower.
Uber in Stockholm is generally overpriced. I know this because i have directly compared trips with regular cab services. All big 3 cab services have apps and the possibility to pre-pay a fixed price. I often go with Taxi Kurir. Try their app alongside Uber.
I use Uber frequently in Stockholm. BUT, in Sweden even Uber cars have to have taxi-regristered cars and therefore it is not as cheap as in other countries. Unless you use UberPOP, then it is very cheap, but there the cars are NOT taxi-registered, so that´s not a good idea.
As other users have mentioned, download the taxi 020 App or the Taxi Stockholm App from Appstore.
How much is a license?
We are leaving the realm of this forum now. However you don't buy licenses, you qualify for them and are tested be a government authority.
I have a seven hour lay over at the airport. December 1. I hate sitting in airport lounges.
Is it worth taking an Uber (or taxi) to Marsta and finding a good Swedish meal in that amount of time?
Other suggestions? (Only site on TripAdvisor is a a Mansion and park, worth an hour?)