Originally Posted by WHBM

There are a huge number of Borises and Natashas in London nowadays, if they chase after you it's probably to put in an offer on your house.

Regarding the OP's question, be aware that although most BA flights from the US do indeed arrive at T4, those from Los Angeles and San Francisco arrive at T1, and from Miami at T3. T1 is an-about 10-minute walk through passages to T3. If you are coming from other BA flights into T4 you do need to take the Heathrow Express train. No fares are charged for the in-airport section from T4 to T1, 2 and 3, just hop on board.

My suggestion for a T3 meeting place would have been exactly the same as YVR Cockroaches. There's a coffee and snack counter there (few airports are so sensible as to provide this at the meeting area - Heathrow's not ALL bad) and the seating gives a view of passengers as they come out. Be aware it's quite a large overall area and there are usually hundreds of people milling about.

The details of the T3 arriving flights are displayed on screens but if you want to know progress of a flight arriving at another terminal go to the airport information counter next to the seating area and they will look it up for you.