we are arriving next summer on at Sat at 9 PM Heathrow (from Copenhagen). We want to see Big Ben, ride a Red city bus and see British Museum. We fly out next day-Sun. 6:30 PM. Which is better--staying near British Museum and using tube to Holborn station or staying near Victoria Station (and how to get there from Heathrow)? We obviously have to get from Big Ben (near Victoria) to British Museum and would have luggage for the Sun flight, which we could take on a bus to Big Ben, but not to British Museum. We do not want the Heathrow Express-6 people too much $$.
Elaine,
If you can manage your luggage, then I'd just suggest that you stay somewhere close to a stop on the Piccadilly line. Holborn would be fine, but you could just as easily stay somewhere like Earl's Court or Gloucester Road or Kings Cross and use the tube. There is really no need to drag your luggage around on Sunday. Leave at your hotel and pick it up on the way to the airport. Most (but not all) hotels will do this for you.
I always take the tube into London. Taking the Heathrow Connect and transferring to the tube at Paddington really would not save you any time over taking the tube directly from Heathrow if you are staying on the Piccadilly line.
The Houses of Parliament (and Big Ben) are closer to the Westminster stop than Victoria.
As others have said, most hotels will hold your luggage after you check out. However, there are left luggage facilities at both Victoria train station and Victoria coach station. (Cheaper at the coach station.)
To get to Victoria from Heathrow take the Piccadilly line to Hammersmith, walk a few feet to to the other side of the platform, and take the District line to Victoria. The current single fare is 4 GBP.
For getting around on Sunday buy a one-day, zone 1-6, off-peak travelcard at any tube station. It will cover all your tube and bus rides during the day and your ride to Heathrow. The current price is 7.50 GBP.
New fares will go into effect in January.