I am considering a flight that will put me in for a 7 1/2 layover in Amsterdam. Would that give me enough time to go to the city for a quick tour?
It might. The train station is right in the airport and it is a short trip into the Centraal Station which puts you right beside the tram termini where you can get a tram almost anywhere. You can also walk from there and you can take a canal boat trip from a stop not too far away.
Just make sure you check the return train times so you are in plenty time for your connection.
That's plenty of time for quick trip into the city. If you need to store any carry-on baggage, don't use the lockers at Centraal Station as they only accept European credit cards with smart chips. Instead use the luggage hold at the Schipol Mall section of the airport.
I was able to use a locker at the Central Station and I don't have a European credit card.
They installed new hi-tech lockers at Centraal Station, and they are less than a year old. Most other stations in Holland have these new lockers as well. You can get around this by purchasing a prepaid debit card at the ticket windows. A 10 euro card costs 12 euros. There is a large sign in English which explains the process.
Anyway, it's easier to leave the carry-on in a locker at the airport. That's what I always do. Last time, I think it was 10 euro, maybe less - coins only. I didn't have any euros, so I went to one of the shops, bought a bottle of water with a $50 bill, took my change in euros, with enough coins for the locker. That also gave me the cash for the train ticket and incidentals. Once you leave the airport, dollars are useless.