Are you eligible for need-based financial aid?
If you want to attend a private university for under 40K/year, and your Expected Family Contribution is higher than your budget, then you will need significant merit aid. That goal is incompatible with applying to reach schools that either don’t give merit (for example, Ivies) or won’t give large merit awards for your stats (for example, UChicago, Northeastern, Villanova).
As noted above, it is likely that the most competitive schools you could attend for under 40K/year will be Pitt and Penn State. Sure, there are both private and OOS public schools where you could get down to your price point, but they won’t be more competitive than your state flagships.
Temple would be another affordable option, if you want to be in Philly. You’re fine for general admissions there (but apply EA for better merit chances); Honors College would be a reach. (From the Temple website: “For Fall 2020, the average SAT for Honors students was 1448/1600, ACT was 32, and average unweighted high-school GPA is 3.94/4.0.”)
You’d be looking for 30K/year or more in merit, to make a private school affordable - to get that, you’ll need to be well above average for that school, which I suspect means that you would consider it a “lower” school. For OOS publics, there are definitely options that merit would bring into range, but again they wouldn’t be higher-ranked than your in-state publics.
Now, if you qualify for need-based aid and your EFC is under 40K, then that’s a whole different scenario. There probably are full-need-met private colleges that you could get into, and be guaranteed enough aid to attend. These probably aren’t Ivies or UChicago, but there are excellent options if that’s your situation. So, you’ll get better targeted advice here if you clarify which financial category you fall into.
What are your goals, career/major wise?
What are the attributes that you like about Villanova? Is it that you want to be in Philadelphia, or that you would like a Catholic university, or one with a good business program, or one with a good basketball team, or… is it just the perceived prestige factor? Again, if we know more about what exactly you’re looking for, it will be easier to make good suggestions.
Also, breaking your arm is unlikely to be a good essay topic. The essay should show why you would be an asset to a college community. Being a man down in debate could be a good topic, if it allows you to paint a picture of who you are as a person and what you learned from that situation.