Don't do cardio before a weights session. It can lead to injury.. and you wouldn't be able to lift to your abilities because energy would be wasted on the cardio.. and you'd also be preparing the body to do resistance training in a catabolic state.. which isn't desirable.
So if anything.. do the cardio after your weights session - not before.
You can do HIIT sessions on off days if you like.. a couple during the week. An HIIT (High Intensity INTERVAL Training) session should be 20min. MAX. If more than that then I don't believe you're doing it very well.
A simple example of HIIT would be sprinting.
So you set up a distance.. sprint it like mad (after being warmed up).. walk back... sprint again 'balls to the wall'.. then walk back.. sprint again balls to the wall and walk back.. repeat until desired time limit (20min. max. imo).. at the end.. if you're as fast as a turtle.. then that's fine.. as long as you're going at your 'max'.
That's basically HIIT
You can do sprints, hill sprints, cycling, skipping, etc. for HIIT.
And I'd also treat it like a weights session, in terms of workout nutrition.. but that's my opinion.
Steady state cardio also has it's place.. if you like to do lots of it and/or have a certain fitness-related goal in mind that recquires a lot of it.. then you can always eat to 'make up' for it. Diet and training all tie in with each other.. so don't worry.. you can generally adjust one to accomodate the other so-to-speak.
In the end it depends on preference and/or what works best for the individual.