Odense has been a building site in the inner city for years. That means two things for tenants: newer lets with elevator and balcony arrive, and there is still noise, scaffolding and diverted routes close to the most central addresses. A cheap 2-room with a view of a hole in the ground is not the same home as in the photo from a viewing three months earlier. Ask about construction work and when it ends.
The older courtyard blocks by the river and in the inner streets have charm, draught and often no elevator. They are the right choice if you want to live in the dense city and can carry shopping up stairs. They are the wrong choice if you have a pram or a bad back and had imagined that Odense C automatically means modern. Standard and floor explain a large part of the price difference between two Odense flats with the same number of rooms.
SDU, the light rail and the station pull in three directions. A household with one student and one train commuter has to choose a compromise — typically close to a light-rail stop that also hits the platform within a few minutes. Two students on campus can drop the inner city. Two commuters towards Jutland can drop the SDU side. There is not one right Odense; there is a right cut for your week.
Have documentation ready, and read about fixed terms around semester start. Odense does not get Copenhagen’s volume, so you cannot count on next week offering five other 3-room homes in the same district. Save the search, and write when the mix of light-rail stop, rooms and rent actually sits on the list.