Gatwick to near Heathrow

What is 'best' to you?

Cheapest? Fastest? Least effort?

How many to transport?
What time of day?

The easiest way to get from Gatwick is to take a bus to Heathrow Airport. Then catch a cab to the property on the NE side of the airport.

There are buses that frequent the area, but they're just too complicated to deal with.

There are numeous ways:

As already mentioned, a coach (bus) from Gatwick to Heathrow Airport. Then either a taxi or Hoppa bus to the Premier Inn.

You could also pre-arrange a car service to drive you from Gatwick to your hotel. You would know the price when you book.

The most expensive would be to hail a taxi at Gatwick and have them drive you.

Lastly, you could take a train from Gatwick to either Victoria Station or St. Pancras and then switch to the Underground. (The tube). But I don't recommend this as it will take the longest and have the most hassles.

If I were doing this I'd probably take the coach, unless traffic was not behaving itself, when I would take a Thameslink train to Farringdon and change there for the Elizabeth line. Onwards travel from Heathrow to the hotel? Well I'd take the local bus (105/111) but taxi/Hoppa are good if tired out by then. But as Frank indicates there are other alternatives.

if doing it by train the fastest and easiest would be Thameslink train (not the Gatwick Express nor the Southern service to Victoria) to Farringdon (after Blackfriars and City Thameslink and before St Pancras) where an easy change puts you on the Elizabeth Line to Heathrow, whence the cab or Hoppa Bus.

If you are looking but not paid already you might consider the Premier Inn at Terminal 4, the Elizabeth Line ends at T4 and it is a short 10 minute walk in a covered above ground tunnel to the door of that T4 Premier Inn. That same covered walkway also has a Hilton and Holiday Inn Express and Crowne Plaza a little closer to the terminal.

Which terminal will you need for your flight?