In San Francisco if you start from St. Mary's: UCSF is 1.1 miles away
by car, CPMC Davies is 1.5. If you start at Kaiser's Geary campus: UCSF Mt. Zion is 0.4 miles away, St. Mary's is 1.1 miles away. If you start at SF General: St Luke's and UCSF Children's Hospital are 1.5 miles away – although UCSF only takes pediatric patients and I think Sutter closed the ER at St Luke's because focusing on specialists is more profitable.
In Oakland: Kaiser and Summit ERs are about half a mile from each other and UCSF Children's Hospital is about 1.5 miles away.
Lower Manhattan: Mt Sinai Beth Israel and Bellevue are about a mile away and there's a VA hospital with an ER next to Bellevue.
In Chicago: UI and county are 0.6 miles away by car and Rush is on the other side about 0.4 miles away. UI actually calls this the "Illinois Medical District".
In Seattle: Swedish First Hill and Virginia Mason are 0.4 miles apart. Kindred's right there too but doesn't have an emergency department. UW Harborview does have an ED and is 0.4 miles in the other direction.