On Planets or Moons
Transport on planets varies greatly from place to place. The availability of cheap near-room-temperature superconductors has made magnetic levitation trains very practical, and exceedingly fast on worlds with thin atmospheres or hosting cultures with a propensity for extensive infrastructure construction.
Interplanetary
Travel within a starsystem is relatively common and though most of it is for some work-related purpose, occasional travel for tourism purposes is within the economic reach of most people. Most inhabited planets have a number of orbital facilities, reached by some combination of single-stage to orbit vehicles (often spaceplanes), space elevators, and space fountains. Facilities on moons and stations at Lagrangian points are also common, and can be reached by short trips with efficient and relatively inexpensive drives.
Interstellar
Comparatively few people have reasons to make frequent interstellar flights, but there are enough that such a service is commercially viable for a small number of entities. Well-heeled passengers may travel on relatively luxurious "flying hotels," on fast brachistochrones, but most passengers travel in hibernation aboard sleeper ships, loaded aboard already in hibernation and packed into specialized hibernacula. For trips that are not popular enough to sustain either category of service, passengers may travel on crewed cargo ships (which are more common in less well-trod regions where local maintenance drone control facilities may not be available to support automated ships), irregular or chartered passenger ships, or on military vessels. (The required political clout is fairly modest; the AWSF is used to having some civilians onboard its ships anyway since it sometimes needs to transport families of its servicemembers to new deployments.)