The University of Wyoming is ABET accredited for mechanical engineering and for several other types of engineering. It would be a very good choice. With you being in-state, and 2nd in your class of 220, with a 34 ACT, I would expect that admissions is either very likely or (I hope) certain, and affordability is also either very likely or certain. I think that you can do very well with an engineering degree from U. Wyoming.
Attending U.Wyoming and taking a semester or a year abroad or at another cooperating university might be something to at least think about.
You are from a WICHE/WUE state. WUE is of course the undergraduate part of WICHE. While I am not familiar with WUE (I am more familiar with a subset of the graduate part of WICHE), this might make some other schools relatively affordable for you. However, I do not see any WUE schools on your list unless I am missing something. Just as one example, Colorado State is a WUE school, and I see on the Colorado State University website to apply by January 15 “to receive full admission consideration and automatic scholarship review“.
You should be able to get accepted to a very good program that will meet a 40k/year budget. You should be very cautious about taking on loans. Loans can for example significantly limit your options after getting your bachelor’s degree when deciding which job to take.
Similarly, while a master’s degree is not needed for engineering, there are some very good one year master’s degrees and having debt can make these unaffordable. Even somewhere like Stanford for a master’s might be possible if you can afford it and if you were to do very well at Wyoming, assuming that you also have very good internship or work experience (Stanford has a 45-unit program which some strong students will do with five classes at a time in three quarters = one academic year, although some students will take an extra quarter, for example possibly over the summer, which is entirely fine if you can afford to do so).
UCLA is a very good university. Admissions is a reach. It will be very expensive. I do not think that it will be worth the cost as an out of state student with a $40k/year budget.
Also, there is absolutely no way that you should start any bachelor’s degree program that will require debt without being very sure that you will be able to borrow enough money to complete the degree. It is possible to get part way through a degree, and discover that you cannot borrow enough to finish the degree. I have seen this happen. There is a very strict limit on what you can borrow yourself without a parent or other cosigner, and the limit is really not going to make much of a dent into the cost of university.
Also, it is not unheard of for an engineering student to end up taking one or two extra semesters to complete their degree. If you are at in-state university, then you will still be in-state for a fifth year if this is needed. If you get financial aid out of state, this might in many cases end after four years. Of course you won’t get financial aid at UCLA, and you probably shouldn’t want to try to afford it anyway.
To me this seems weird. However, universities will not penalize you for the limitations of your high school. If they do not offer AP classes, then you do not take AP classes. Also, for a potential engineering major, I do not think that anyone would expect you to take AP Art unless you just happen to want to do it.
For engineering it is valuable to have done well in math classes in high school, and also in physics. With an unweighted 3.97 GPA, it looks like you have done well in everything, including math and physics.
I think that you are doing very well, and are likely to do well in university regardless of where you attend. However, do not underestimate the quality of your in-state flagship, and do not underestimate the significant advantages of graduating university debt-free.
There is one more thing that might be worth adding: Sometimes we see students who don’t want to attend their in-state public university because they feel that their excellent high school results should allow them to go elsewhere. However, where you go to university should be at most second or third on the list of the reasons to want to do well in high school. Number 1 is that your excellent results from high school, and the hard work that made this possible, have set you up to be ready to do well in university. Engineering classes are not easy anywhere. It certainly looks like you are ready to take on these tough engineering classes, whether at Wyoming, Princeton, or anywhere else. The second issue is that doing very well in high school might increase your chances of getting merit based aid at some schools (but not Princeton). This might for example allow you to graduate university without debt, and maybe (?) with some money left in the bank in case you want to consider graduate school (such as a master’s degree) at some point. What university you get accepted to is maybe third on the list of reasons to do well in high school, but only third (or fourth, behind making your parents proud – and I bet that they are).
Best wishes.