As soon as you emerge from the station, you will see a fountain, and beyond it, a castle, which is now a major part of the University buildings. If you walk along the street towards the castle/university you will soon spot the cathedral to your right. In many ways it is architecturally a traditional gothic shape, but it is constructed from red brick. If you walk up the incline to the castle/university itself (which is worth doing for the view of Uppsala but there is not much that you can visit because the historic buildings are in active university use), you will see the botanical gardens in front of you and it is easy to go down to them. When you do so you will be staggered by their size and by the amount of information contained there.
Near the hothouses there is a very pleasant cafe which is not too expensive for some cake and a drink of tea.
The river Fyrisån runs through the centre of the city and there are both pleasant cafes and seats for those with picnics.
From journal Delightful Uppsala