Is Hilton Heathrow convenient to Terminal 4?

It is extremely close to Terminal 4.

I have stayed at several hotels near Heathrow. Renaissance is my favorite. If you like looking at airplanes, their club room looks out on the runway so close like you are in the airport.

I have not stayed at any of the Hiltons near the airport, so can't say anything about that experience. The one you mention does appear to be very close to the terminal. But that might not make a difference in how long it takes to get to the terminal. I use the bus service which has several different busses running to all of the nearby hotels for a reasonable price (£5 last time I was there). They have their established routes and the hotels nearest the airport might not be the one that is stopped at first. Renaissance is the first stop for that bus from Terminal 4 and the last picked up on the way back (at least it always has been when I stayed there). Taxis seem to take forever no matter which terminal or hotel you are going to.

There is a walkway from the Hilton straight into Terminal 4 (5 minutes from front desk to check in). Most of the other airport hotels are on Bath Road, which is on the other side of the airport and would need a bus or taxi to get to T4. The Hilton is pretty nice. I would switch if you can.

Bath Road hotels are great for Terminals T2/3, so so for T5 and fairly poor for T4, as they are on opposite sides of the airport complex. For that I would always go either for those close in to the terminal (eg Hilton T4 or Yotel etc) or the Hilton Garden Inn near Hatton Cross.

The Hilton and Premier Inn are connected via a walkway. The Yotel is in Terminal 4.

I'm sitting in my room at the T4 Premier Inn at this moment. I timed the walk from the fare gate at the tube station to the front desk of the hotel: 15 minutes. The Hilton is near the Premier Inn. Although it may be a bit closer to the terminal, I don't think it would save more than 1 or 2 minutes of walking time, and I'm sure it is far more expensive than the Premier Inn.