In most places, being within 1 mile of everything you likely need (work, food, etc.) also places you in prime real-estate. And by prime, I mean extremely expensive.
Depends on your definition of expensive. We live in downtown Chicago, but our living expenses (for 2 people) are about $30,000 per year--very achievable in a childless two-income household with Chicago's soon-to-be $15/hr minimum wage. On one hand, my rent is a bit lower than average, but on the other I have an facepunchingly high food budget that could be halved easily--so it probably equals out.
And since everyone else is doing it: Within a mile, I have 2 Targets, 2 Whole Foods, 2 candy stores, 1 Trader Joes, 1 terrible supermarket, 2 good supermarkets, 3 small independently owned supermarkets, about 50 Starbucks (not hyperbole; they're rarely more than 2 blocks apart), and several CVSs and Walgreens. Also, 2 farmers markets, the main branch of the Chicago Public Library, the Chicago Riverwalk, Millennium Park (free concerts!), Grant Park, Chicago Cultural Center, the Art Institute of Chicago, some smaller museums, 2 ice skating rinks, tons of really cool architecture, lot of water features, all of the public transit (including a water taxi), and several university campuses. Hundreds of "neighborhood" restaurants, hundreds of pubs/bars. thousands of chain restaurants, a couple churches, lots of gyms, lots of salons, and way way way too much crap to buy (I'm looking at you, 2 Disney Stores that tempt me so). Stretch to two miles and you've got the Museum of Contemporary Art, Navy Pier, a beach, the lakefront trail, and part of the museum campus.
But. No schools. No real playgrounds. No neighborhood sandlot type places. No bakery. No butcher. No fishmonger. No awesome ethnic supermarkets. No independently owned ice cream joints. No yards. No vegetable gardens. No backyard animal husbandry. No "tribe." No nearby friends, family, or coworkers (downside of working 30 miles from home). No parking for less than $200/month.
Big city living is not for everyone, particularly families with children (although there is a 2-child family on my floor--I suspect they homeschool?), but I think anyone who loves it can make it work. We think about moving to the suburbs--I want a dog and a garden, he wants a car and a man cave. But then we look around us and realize what we'd be giving up--including our smallish annual budget.