Although your budget is rather tight and you have not clearly mentioned if your budget is inclusive/exclusive of airfare, note that travelling in a large group has its own advantage. You can ask for discounted rates for packages, rooms, etc.

Keeping the large group advantage in mind, you can contact a good travel agency to work out a deal for a trip to Bangkok (Thailand). A 5-day trip to Bangkok can be worked out within your budget. Also check the discounted flight + hotel packages offered by reputed online travel agencies (make my trip, yatra, etc.).

Since the hills are ruled out, I cannot suggest Bhutan. But Kathmandu, the capital of Nepal, is a convenient option as you have only four nights to spare. Although Nepal is a mountainous country, travelling in and around Kathmandu will not be a problem for the elderly. There are direct flights to Kathmandu from Kolkata and Delhi (price of a return ticket starts from Rs 8,000+ from Delhi and Rs 10,000+ from Kolkata). For discounted room rates, try to book online but do check the cancellation rules in case anyone opts out at the last moment. Choose a hotel (check that the hotel has an elevator) in the Thamel/Lazimpat area. There are plenty of travel agencies here where you can book sightseeing trips in and around Kathmandu (two days), Bhaktapur and Patan (one day). The area is also a great food and shopping hub (you can buy almost everything, from branded products to locally made handicrafts).