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I would say, if you are looking for something similar climate wise but not to the extremes you've described, the Midwest would probably be where you want to narrow your search. In the midwest, at that point it can literally be pick and choose. All of the major areas offer what you are looking for from shopping to schools. It would literally come down to the most minute things such as topography. Obviously if being by a large body of water is important, Milwaukee and Cleveland automatically comes to mind. Metro Detroit sounds like a great fit for you as well. If you are really wanting to pursue your Architecture Engineering path then Chicago is going to be your best bet followed by Kansas City. Chicago is expensive only by Midwest standards, other than that when compared to the rest of the US, it is pretty cheap and while large in area (city and suburbs), it is very easy to navigate and shouldn't worry about getting lost there and almost impossible to get lost on the Indiana side.
In the end, every area in the midwest will offer high end shopping, good schools in the burbs and areas of safety and reasonable pricing. I would actually rank the things that are truly important to me from 1-100 or whatever number you end up with down to the finest detail because a lot of areas within the United States fits your general criteria.
You can still live outside of NYC and have the big city life but live in the suburbs more affordably. Long Island is great, Westchester, New Jersey. It's suburban life outside a big city without all the city hulabaloo. And if the OP is beach person we have great beaches that are very close.
NJ & LI schools are rated highest in the nation.
The OP also mentioned s/he didn't want an extreme climate. The NYC metro doesn't have a mild climate.
You'll certainly hear bad things about the climate of Seattle (and Portland) but you should consider whether the "bad" parts bother you. The Northwest gets a lot of cloudy, gray, drizzly, rainy days. But on the good side, the temperatures rarely go above 90F or below freezing (each happens maybe once or twice a year). Many people love the climate here.
Also, Portland is closer to the size you're looking for.
Seattle is is 55 degees and pouring rain right now. It's late June in the afternoon. I'm inside with the gas fireplace on. It may not be extremely hot or extremely cold, but it is extremely miserable. Not sure why other posters keep trying to talk others into moving here. There are a group of people who think 70 degrees is too hot and 15 minutes of sun is burning their skin. Seattle is ideal to them. It's a great city in so many ways, but the weather here should be a HUGE consideration.
Seattle is is 55 degees and pouring rain right now. It's late June in the afternoon. I'm inside with the gas fireplace on. It may not be extremely hot or extremely cold, but it is extremely miserable. Not sure why other posters keep trying to talk others into moving here. There are a group of people who think 70 degrees is too hot and 15 minutes of sun is burning their skin. Seattle is ideal to them. It's a great city in so many ways, but the weather here should be a HUGE consideration.
its sunny and 85 degrees right now in Indianapolis plus we dont have to worry about having a high cost of living and we have the nations most affordable housing market.
And were only a 3 hour drive from Chicago which is a nice bonus. or a days drive to 80% of the US population.
I wouldn't call the climate of NYC metro "extreme"
In the summer it is in the 90s F with high humidity (so it feels above 100 during heatwave days) and in the winter if can definitely drop below the freezing mark and feel colder due to the winter. When it snows there is ice and slush that can hinder one walking around the streets (especially crossing the streets) for days besides drivers have to dig their cars out of the snow. I don't consider any of this to be a mild climate.
In the summer it is in the 90s F with high humidity (so it feels above 100 during heatwave days) and in the winter if can definitely drop below the freezing mark and feel colder due to the winter. When it snows there is ice and slush that can hinder one walking around the streets (especially crossing the streets) for days besides drivers have to dig their cars out of the snow. I don't consider any of this to be a mild climate.
It maybe reaches 90 3 or 4 days out of the summer... most of the time it is mid-80's. Yes it's all humid, but most of the entire east coast is.
We got one big snowfall this past winter... ONE.
The midwest gets far more snow then we do. Flagstaff, AZ sees the highest amount of snowfall and it is over 100 degrees almost everyday there. The NYC area is definitely not as extreme as some other areas.
its sunny and 85 degrees right now in Indianapolis plus we dont have to worry about having a high cost of living and we have the nations most affordable housing market.
And were only a 3 hour drive from Chicago which is a nice bonus. or a days drive to 80% of the US population.
You get what you pay for is all I have to say... not knocking, as I have never been to Indy but the NYC metro is very expensive b/c it is very very desirable and beautiful. Do you have ocean beaches in Indy?
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plus we dont have to worry about having a high cost of living and we have the nations most affordable housing market. 
