I suggest that you remove London Heathrow airport from this list right away, since it is the only one of the four airports you mention for which you will need a transit visa. You don’t need transit visas to stay in either Zurich Airport or Amsterdam Schiphol, nor even at Ataturk Airport in Istanbul since you will have a US visa. All three airports offer in-airport hotel facilities to transit passengers. But the most promising (and affordable) seem to be at Zurich. Their Transit Hotel offers passengers useful facilities, ranging from basic but private single/double/triple rooms as well as couches on which you can stretch out and catch forty winks in their Rest Area. All of these are chargeable depending on the number of hours you need them and whether in the day or night (triple rooms, for instance, cost CHF 99 (approx. ?6,800) for six hours in the day; a couch between CHF 20 and 40 (?1,390-2,000) in the day). Details and a downloadable price list are available at https://www.zurich-airport.com/passengers-and-visitors/airportservices-en/layover-and-lounges/transit-hotel-bedrooms. Do book your choice well in advance as I would imagine these are popular and you won’t want to be turned away bleary-eyed.

At Amsterdam Schiphol, a triple room at the in-airport Mercure Hotel will cost approximately ?10,000. See details at http://www.schiphol.nl/Travellers/TravelAgencySchiphol. nl/HotelsAtSchiphol.htm. The TAV Airport Hotel Istanbul in Ataturk Airport offers only single and double rooms, and charges according to the number of hours they are used. Rates start from ?13,600 for a double used for 6-9 hours. See http://www.ataturkairport.com/en-EN/shoppingdinning/pages/airporthotel.aspx.