BA has a bewildering number of ways to find reward availability. I'm quite new to the reward flights game, but this is what I've discovered so far:

BA website (desktop and mobile):
- Reward Flight Finder lets you search by a wide rage of dates and/or destinations, including searches by continent. The continent search is more limited than the city search as it's only possible to see one month's availability at a time. You can't see partner or connecting flights.
- Search and Book only lets you view one day at a time but includes partner airlines and connecting flights.

BA app (Android and iPhone)
- Reward Flight Finder lets you search by a wide rage of dates and/or destinations, including searches by continent. Unlike the website, the continent search allows you to see a full year at a time but the interface is a littlew clunky with lots of sideways scrolling. Again, you can't see partner or connecting flights.
- Standard Avios Search simply redirects you to the website, from which you can access the desktop version. It's slightly clunky on a mobile screen but can be useful as the sideways scrolling is less awkward than the mobile version.

BA Executive Club app (Android and iPhone) gives a month-by-month view of the number of seats available to a specific destination.

As mentioned above, there are also numerous third party tools available including partner airline websites. Personally, as I have never bothered to set up any alerts as my travel dates are quite flexible, I've never found that they offer much more than BA's own desktop Reward Flight Finder.