I spent my 12th grade year abroad, and had a great time. If there is any way you can find an "organized" program, rather than just bumming around, I'd say go for it!
In addition to the organized HS year abroad, I spent a year abroad as an undergrad, through my university, and then I later attempted my doctorate abroad ... on my own.
Comparing the three experiences, the organized HS program enabled me to learn the language better, and integrate me into native life better than time on my own. The undergrad program was just a chance to go out barcrawling with other North Americans, and the doctoral experience... well, something else entirely.
I know there are a few good programs with non-profit organizations. Try websearching "13th year abroad" or "13th grade abroad". I also know a few people who completed 12th grade at home, and then went to another country, and completed 12th grade there, allowing them to go to university in another country (if you get a European high school diploma, studying anywhere in the EU becomes much easier). Do you research! But be quick - usually the deadline is in February or March for the upcoming fall.