To answer your question, mathematically, it should be possible to get to a 3.0 if you ace your junior year. Just as a rough calculation, if you had the same number of credits every year and got a 4.0 UW in the third year, it would get you to a 3.18 UW. Hitting the 3.0 mark would help you a lot with college admissions, and a strong upward trend casts any GPA in a much more positive light than otherwise.
The question is whether you can keep your upward trend going. There’s no way to tell that from what you’ve posted here. Your particularly “off” freshman year, combined with your parents’ stringent requirement that you remain close by, suggests that maybe they’ve had reason to be concerned about you. The important perspective to have is that you can always get a fresh start on school, even if it means attending somewhere that isn’t what you might have imagined for yourself. Making sure that you’re in a good place in terms of your overall health and wellness is what is most important. And part of that is setting realistic goals, not setting yourself up for a crisis by getting in your head that you must now get flawless grades or your life will be ruined. Resolve to do better, and be thoughtful about how you can set yourself up for success; but don’t set goals that hinge on perfection. Set realistic goals, and then if you exceed them, that’s great!
I still think the competitive private U’s in the Boston area are likely to be out of reach. (No harm in trying, but it’s a steep admissions path made even steeper by the sheer numbers of students who want to go to college in Boston.) But you’ll have options. How about UMass Dartmouth? It’s within your parents’ desired radius, and 75% of first-years live on campus, so it’s not purely a commuter school. It has a business school https://www.umassd.edu/charlton/ and you’d probably have transfer potential within the UMass system if you did well and didn’t want to do all four years there. I don’t know if business is a lot harder to get into than the campus in general, but you can probably look into it and find that out. At any rate I think it’s the most forgiving of the UMass campuses, stats-wise, and they have the “Connect” alternative entry program for students who don’t meet the thresholds for regular admission.
Another option Dean College. I knew a young man who struggled in high school, some years back, did a two-year program at Dean, and then transferred to UMass Amherst and got his degree from there. They have both associate and bachelor’s programs in a number of business-related areas, and they offer a high level of support and individual attention.
A good reachier school to shoot for could be Clark University in Worcester. They have an undergraduate Management major, and students who do well can qualify for their 5-year BA/MBA program with the fifth year free. https://www.clarku.edu/programs/major-or-minor-management They made Forbes’ “Top 20 Entrepreneurial Universities” list, and while it will be a reach for your GPA, admissions are holistic, so with an upward trend, and good EC’s and test scores, it could certainly be a possibility.
Providence College would also be within your 1-hr radius of Boston, in the away-from-NH direction, and has business-y majors. Again, a stretch, but if your tests scores are high and grade trend is upward, it could work.
Lastly, if your grades continue to improve and you really want to try to crack a higher competitiveness tier, consider looking into productive gap-year possibilities. To maintain your eligibility as a freshman applicant, you would have to avoid taking college-credit classes during that year. But you could study a foreign language, do an internship, participate in a service program like City Year, anything that does not involve enrolling in college. This would allow you to apply with your full four-year high school record complete, which could be a help if you do well both junior and senior years. If you got into, for example, UMass Dartmouth Connect, as a senior, you could deposit there and defer your admission for a year, so you’d still have that as a backup, and then apply to more competitive programs during your gap year.