For museums and universities, cosmopolitan feel, variety of restaurants and ethnic groceries and communities, and a fairly liberal political landscape, how about Chicago?
Winters are cold and go from late November to March, more or less. Summers are very much appreciated.
Property taxes are high in the municipalities where schools are good - the taxes pay for the good schools and other public facilities, and services like the police force.
Here's an idea of the facilities in the very mixed income, progressive (it is known as 'The People's Republic of X') and determinedly desegregated suburb where I live:
Huge main library and two branch libraries
Park District that runs -
A multitude of after school and preschool activities and classes year round
Two outdoor public pools, both with baby/toddler area, water slides
Indoor recreation areas for boy scout and girl scout groups and also for organised classes offered by the Park District for all ages
Public tennis courts
Public baseball/softball/t-ball fields, soccer fields, basketball courts, playgrounds, skate park
Gymnastics centre
Year round ice rink
A few dog parks
A conservatory
Chaperoned getaways like all night skiing for teens
Activities are non-stop for all ages.
The public school facilities are out of this world. I was gobsmacked when I was what was offered. There is a huge range of extra curriculars and a high level of participation. My DCs got tired of hearing me tell them how lucky they were. I can only imagine what I would have had to pay for similar educational environment in Ireland (where I am from). Actually I know what my Dsis pays for a fraction of what my DCs get so I don't have to imagine. Best of all, I found the teachers and counsellors incredibly positive and professional and dedicated to each child's success. I love the GPA system, having been through the Irish Leaving Cert and Matric. And there's no uniform!
In approximately 4.5 square miles there are between 50,000 and 60,000 residents, several separate shopping areas, several supermarkets, two local/city train lines and one regional line, bus service in all directions, over 50 houses of worship, 20 languages are spoken in homes, huge income diversity, three theatres, a semi art house cinema (something for everyone), a renowned children's choir, a symphony orchestra, bike lanes on major streets, 'Divvy' rent a bike locations, neighbourhood organisations, sport organisations with volunteer coaches, busy PTOs, great independent ice cream and local pizza places and small bookshops, art supply shops, private schools of many stripes including religion based and Montessori and excellent public schools.
People shovel the sidewalks when it snows, and children play out in front of their houses. There are alleys in the back where the garages open onto, and people put up basketball hoops there for pretty much public use. There is a relaxed attitude to children retrieving balls from other people's yards, neighbours tend to know each other and each others' children, and people care about the schools.
I agree that you need to approach Americans with an open mind and focus on the positive. People don't like to hear how much their healthcare system sucks or how much better British people drive, etc. People like to go along and get along, and tend to steer clear of controversial topics of conversation - religion and politics really are sort of taboo in a diverse society and people value harmonious interaction. Be curious and smile, and try not to come across as judgey.
Wrt the cost of third level education:
State schools can be a real bargain.
If you plan on settling, do remember that your child might be able to avail of a terrific university opportunity in Michigan, Virginia, California, Illinois, Ohio, Minnesota, Wisconsin, (yes) Texas, New York, Washington (the state) and North Carolina, for a lot less than a private university would cost. US universities also offer financial aid that is needs based.
'Junior college' is a community college, offering two year associates degrees. Credits can sometimes be applied to bachelors degrees at four year institutions. They also offer technical courses like EMT training and LPN qualifications. They are not universities.