I really love living close to to a large city now because of the endless opportunities and options, so I’m looking for some relatively competitive colleges that are located near a big city, but not in it.
It would be preferable if there was some sort of public transportation to get to said big city from the school, and if the school was on either coast, (east/west).
Any ideas? Thanks in advance!
Use the CC college search tool and select suburban campus location.
You could also search: “The 25 Most Desirable Suburban Schools / Newsweek.”
Selective colleges located more or less near major ~coastal cities include:
Tufts and Wellesley (near Boston)
Boston College
Sarah Lawrence (~20 mi from NYC)
Princeton (~50 mi from NYC)
Bryn Mawr, Haverford and Swarthmore (near Philadelphia)
University of Maryland (DC outskirts)
American U (in a ~residential area on the edge of DC)
Emory (near Atlanta)
Stanford (~35 mi from San Francisco)
the Claremont colleges (~30 mi from LA)
Some schools in the University of California system might satisfy, too.
If midwestern colleges are acceptable, add Northwestern (near Chicago).
Look at Lewis and Clark in Portland OR. I think many of the ones mentioned by @tk21769 will be huge reaches for the OP.
Reed is also in Portland.
Brandeis is also near Boston.
What sort of stats do you have? If you are looking for some less selective options, consider Drew (Madison, NJ, with easy rail access to NYC) or Lake Forest (very close to Chicago).
Macalester in St. Paul
I love Tufts and Macalester. 
@woogzmama, sorry this is such a late response, but I have a 33 ACT and weighted GPA is a 4.16. I’m Asian/Hispanic.
Holy Cross, Brandeis.