Why there is no single answer
A 1200 is not good or bad on its own. It is good relative to some colleges' admitted classes and weak relative to others. A score that puts you above the median at a large public university can sit below the 25th percentile at a highly selective one. The question is not what 1200 means in general, it is what 1200 means for the schools on your list.
We are not going to state where 1200 falls on a national percentile table here, because that number moves from year to year and College Board publishes more than one version depending on which population it is compared against. Look up the current official percentile table on College Board's site if you want that specific comparison.
How to check if 1200 is good for your list
Every college publishes a Common Data Set, and section C9 lists the 25th and 75th percentile SAT scores of its most recently enrolled class. Search the college name plus common data set, or plus class profile, and you get numbers straight from the school rather than a third party estimate.
If 1200 is at or above a school's 75th percentile, your score is a strength in that application. If it falls below the 25th percentile, it is a weak point the rest of your application will need to make up for. Anywhere in between is roughly neutral.
What 1200 looks like by section
The total score is the sum of two section scores, Reading and Writing and Math, each scored from 200 to 800. A 1200 could be an even split, roughly 600 and 600, or lopsided, like 680 Math and 520 Reading and Writing. Colleges see both numbers, not just the total, so a lopsided score reads differently depending on what you are applying to study.
If you are well short of an even split, the lower section is usually the faster place to gain points, since it has more room before it hits its own ceiling.
Test optional and scholarships
At schools that do not require a score, the real question is whether submitting 1200 helps or hurts your application. A common rule of thumb is to submit if you are at or above the school's median and to consider withholding if you are well under the 25th percentile, but policies and what counts as median change yearly, so check the admissions page for the year you are applying.
Scholarships are a separate track worth checking directly. Some state schools and merit programs publish specific score thresholds that unlock award money, and those thresholds are usually stated plainly on the financial aid page rather than needing you to estimate anything.
If you want to move past 1200
Improvement from a 1200 baseline usually comes from closing the gap on your weaker section first, since raising a 520 to 600 is more available than raising a 680 to 760. Skill level practice, drilling one topic at a time and reviewing why each miss happened, is what closes that gap fastest, more than repeatedly taking full tests without reviewing them.
StudyPebble offers free daily practice organized by the same skills College Board tests, with an explanation on every question you miss. It is not a substitute for full length practice tests in Bluebook, but it is a place to drill the specific skill that is costing you points.