One Night in London

If it were me, I would book into a hotel near the airport, toss my bags into my room, have a large cup of caffeine, and head into town for dinner and a walk! Back to the hotel late, sleep and up early to catch the flight to Croatia.
From Heathrow you can take the tube straight to Green Park Station (30-40 mins.; Buckingham Palace, the Ritz, St James Park) or a few more stops to Leicester Square (Trafalgar Square), or one more stop to Covent Garden (Theater District, restaurants). You could also change at Green Park and go to Westminster (Houses of Parliament/Big Ben. Westminster Abbey, the Thames and the London Eye). All these places are great for a walk around and dinner somewhere nice!

Thanks! Sounds like a great plan.

I would stay in a hotel off the Picadilly Line so you can take the tube to your hotel on arrival at Heathrow, check in and drop your bags off, then be on your way for some sight seeing! One thing, once you arrive at your hotel, DO NOT, I repeat, DO NOT lay down on that bed! Its going to be tempting since you'll be tired and sluggish. Instead freshen up and have a plan and head out to explore. If this is your first time in London, post it and we'll give you some lovely ideas. Most sites/museums close by 5 pm, although some do close late on certain nights of the week so you can check on that. Even with those closings, there is so much to see in London. You might want to consider the Eye which is a quintessential London tourist stop then a walk along South Bank.

Oh yes.... we'll definitely stay away from the bed. This is our first time in London, so any suggestions for filling in a few hours in the late afternoon/early evening would be greatly appreciated. We are fit and happy to walk.

You could also change at Green Park and go to Westminster

I would change a bit earlier. At Gloucester Road, South Kensington, or Sloane Square. See http://www.tfl.gov.uk/maps/track/tube

Unless you need the elevator for disabled access.