How to find availability to spend your British Airways airmails (Avios)...
Avios seats first become available 355 days before departure - the earlier you book, the better chance you have of getting the flight you want.
Try to be flexible - although I appreciate this is easier said that done if you have family and need to travel at certain times of the year.
If you travel off-peak it will cost you less Avios.
If you want to go to New York and there is no availability, have you considered Boston, Philadelphia or Washington - they are all close by (train or a short internal flight) and it's an opportunity to spend a few days in different city.
If you can't get a return flight in and out of New York, try looking for availability into New York and out of a different city.
The best place to check for availability is not British Airways own website, but a third party site called BA redemption finder. it's a really simple site that shows you Avios seat availability for the next 355 days and it can be found here:
Once you have found availability, head to British Airways website, log into your Executive account and book your flight through the Spending Avios link.
If you are having difficulties or are booking a complex trip, you can phone British Airways and get an agent to help you (although you typically get charged a £35 per person admin fee for this).