Small side trips traveling between US & India

When traveling from US to India, I know that its very easy to have a short tourist stop in

• Singapore: Stopovers >3hrs(?) get a free tour of the city
• Hong Kong: Visa on arrival, on an 8hr stopover I could get a visa and sightsee

As an Indian citizen with US Green Card (permanent residency), which other tourist destinations can be considered for such a trip, by perhaps going for slightly longer stopover and a specific airline to visit a city at minimal extra cost?

I'm looking for options that

• don't require visa or allow visa on arrival (no advance planning needed)
• easy for a tourist to sightsee (availability of guided tours, or safe to roam the city)
• since its for small stopovers, excepting visa & local tourism cost it should be minimal added expense
• given above point, I'd expect such locations would probably be a hub for airlines flying US->India, or close to one?

Places such as UAE that need a little preparation afaik (invitation by residents or hotel booking) can also be mentioned as it would help others.