First, the airside parts of Heathrow close over night. So you will have to leave the airport via immigration whether or not you want to.
In your circumstance (Indian passport, holding a valid entry visa to the USA), you will be permitted to enter the United Kingdom for transit purposes providing you leave again the next day.
You do not need a visa, but you do need proof of your onward travel. A printed copy of your itinerary should suffice.
Here is the official information:
Visa required, except for Passengers holding confirmed onward
tickets passing through United Kingdom immigration to make a
landside transit to a third country on a flight that departs
before 23:59 the next day. The following conditions must be
- passenger must arrive and depart by air; and
- passenger must have no purpose in entering the United
Kingdom other than to pass through in transit; and
- passenger must hold all documents required for the next
- passenger must pass through United Kingdom Immigration; and
- passenger travels with a document listed in the following
- ***Warning*** Passengers may make a landside transit if
holding a valid visa which allows entry into Australia,
Canada, New Zealand or USA and traveling as part of a
journey to, from or transit through the country that has
issued the visa.
Once you have entered the UK you are free to go to your hotel and do some sightseeing, providing you leave before 23:59 the next day.