There are no guarantees, each monitor is an individual and will have its own personality. That said, some species tend to grow more trusting of humans than others. You might look in to savanna monitors, white throat/black throat monitors, salvator water monitors, desert sand monitors, argus monitors, or Dumeril's monitors, and avoid Nile monitors. Clearly, you will be looking for a larger species, since smaller monitors will tend to get lost if you let them out.
Only let the monitor out for relatively brief periods and only when supervised. These animals can cause an amazing amount of damage - they can tip over shelves, dig up house plants, rip drapes and blinds to shreds, even dig holes in drywall. Further, they do best in hot, sweltering conditions, so leaving them in human-comfortable climates for prolonged periods of time is not good for their health.
You will find monitors are much more active and intelligent than constrictors. They require larger, sturdier enclosures, do best if they have a deep substrate they can dig in, and need higher basking temperatures than are typically used for constrictors. They do not respond well to forced handling, taming a monitor is more a matter of leaving it alone until it comes to trust you and accepts you. Handling when it is stressed by your presence just teaches it that you are a source of bad things and makes it fear you more.
I have had a number of monitors which could roam around the house under supervision, but I kept these excursions fairly brief - essentially "treats" which allowed the lizard to engage its curiosity and explore new places.
I prefer monitors to iguanas as "pets" since male iguanas are prone to unprovoked attacks on humans when in rut. Monitors, at least, only attack if they feel threatened or if they know food is nearby (watch your hands when feeding!). Do be careful and always wear shoes when a monitor is loose on the floor - I've noticed a tendency for monitors to go after bare feet.
Good luck, and if you feel monitors might be right for you or your friend, I would suggest reading the husbandry advice on the Pro Exotics website (probably the best source of monitor husbandry on the web, and much better than any common pet store books, which are largely recipes for how to slowly kill a monitor).
Luke