By taxi
If you would like to travel by taxi, use the four major taxi companies: Uppsala Taxi, Taxi Kurir, Taxi Direkt and Taxi 020. There are also a lot of smaller companies, but they might have their own view on what you should pay and might also have less geographical knowledge. Be sure to negotiate the fare in advance of getting in the taxi if no guaranteed fare is posted.
By bike
The best way to travel in Uppsala is by bike. As any visitor will notice, there are a lot of cyclists here, enough so for the city to earn the nickname "Bike Town." There are paths paralleling nearly every road, and many places to store them outside. Several rental places exist in town. As a side note, locals have a saying that everyone who lives there has had a bike stolen at some point in their lives. While this is not entirely true it's more a reflection on the popularity of biking than any level of crime, it's probably a good idea to lock your bike.