where to stay on a layover in London

I'd think, that with a twenty-four hour layover, you could see quite a bit of London - - depending on your arrival and departure times for each flight. How about specify those and you'll probably get some help. You'll also need to state if you're going to be able to hump your junk while you wander around or need a place to stash it. If you need to chunk it somewhere, how much, what size, etc? One hotel probably won't work for both ends since, again depending on times, you'd probably want to preposition and spend the night close to the departure airport - - but it depends on the times. Fess up.

Taking a trip from the US to Italy, but on both ends I have a 24-hour layover in London. On the way, flying into Heathrow arriving 2:45, leaving next day out of Gatwick at noon. On the way back, flying into Gatwick at 5:00 and leaving next day out of Heathrow at noon. Can't keep luggage with me, as I have elderly mother-in-law in tow. Where should I stay the night that will work with both airports and perhaps allow me a sight or two? Thanks,
Chris

When you say 2:45, is that am or pm? 5:00 am or pm?

I'm considering the same trip. My plan is to arrive at Heathrow then get to Gatwick the same day. Simplest way to get there might be the bus connecting the two airports. There are many hotels and B&Bs near Gatwick; it is my plan to stay in one of them then shuttle to Gatwick airport in the AM. You might want to get situated in a hotel at Gatwick then take the train into London for a few hours, leaving others at the hotel if they haven't the energy for touring. Returning, I would fly into Gatwick then get to a hotel at Heathrow and repeat the process. It is a quick trip by train or Tube into London from Heathrow airport.