I would also make sure you know that Radioactive Iodine is *nothing*, I repeat, NOTHING like radiation for other types of cancer. In other words, no radiation burns, no multiple treatments (usually only one), no fatigue, no risk of hair loss or scaring. I've seen the effect on people going through "real" radiation and believe me, I thank God that I didn't have to go through that.
Basically, the main side-effects are nausea in some people (but not as bad as with normal chemo) and tightness/pain in salivary glans that can be prevented by sucking on sour candy several times a day (which you have to do to clear the RAI out of them anyway). Also, having to be isolated for two days is a draw-back because of the risk of exposure to others because it can damage their thyroid glands.
Personally, I am for it because of the low-risk and positive benefits, such as making the Thyroglobulin test more accurate to test for future cancer growth, that kind of thing. It is, however, your decision and there are a lot of resources out there to research what is best. I think it does depend a lot on how far a long the cancer was and your age. I will also say that I saw some research that said that the greatest predictor of positive outcomes was aggressiveness of treatment.