Public transportation to Hyde Park/Kensington Gardens from Terminal 5 Heathrow

Take the Underground. Picadilly line from Terminal 4 to Hyde Park Corner station. It's an easy walk to either park. Use Google maps and select restaurants near Hyde Park for a multitude of dining options.

Take Elizabeth Line to Paddington station. Exit, easy peasy stroll to the Lancaster Gate Entrance to Hyde Park/Kensington Gardens at the Italian Gardens.

Gates open up at 5am and I believe are locked at midnight.

Spots to eat; Tudkin Flavors of Malaysia, The Victoria Paddington. My go to spots when I stay in the area.

I’d download the TFL app if I were you, just to be on the safe side. It includes a journey planner and a feature called “buses near me” that shows you what lines are close, the stop to walk to, and the direction in which to take the bus.

If you take the tube to Marble Arch Station it would be perfect to alight there and walk through Hyde Park over to Kensington Palace - it’s a lovely, lovely stroll! Once you’ve gotten all the way to Kensington Palace, however, you might want to catch a bus back to the tube. The TFL app will help you do that. Bus 94 leaves from Queensway tube station and takes you back to Marble Arch, for example. There are other options, of course.

Why not take the tube back to Marble Arch? Because the tube can be kind of miserable. I live in west London and I avoid it for short trips. As a tourist, you probably want to see things above ground during your time in London, and a bus is a great way to do that. On short trips, the bus takes about the same time as a tube journey, during which you will be trudging along underground and not seeing the beautiful architecture, cute gardens, and so forth.

Have fun!

The Elizabeth line does not stop at Marble Arch. You could as Claudia says get it to Paddington and walk but I think Bond St is a bit nearer, especially if you sit on the back of the Elizabeth line train.