I am travelling to Nigeria on British Airways from America on 18th December with a stop over for 15hrs waiting before my content flight at Heathrow Airport on 19th December, 2017, can I get a transit visa for sight seeing.?
No. A transit visa is only available if you are in transit within that, you going sight seeing would be in breach of the visa conditions. See this link for more information.
A transit visa will allow you to change airports within the UK, example would be if your flight arrives at Gatwick but your next flight takes off from Heathrow. A transit visa would allow you to leave Gatwick and travel to Heathrow, it would not allow you to stop in London to see some sights.
You could apply for a Visitor in Transit Visa. This will allow you to leave the airport and return again a few hours later. However, if you are from the USA then you might not need a visa at all. The UK and US have a "special relationship" which should allow you entrance to the UK for up to 6 months without a visa.
I suggest you take this short quiz and see what options you are given.