If by falcons you mean birds of prey more generally, it's hard to beat the New Forest. I was dog walking at Acre Down (in the forest) a few years ago and met a man who had been birdwatching since dawn. In the six or so hours that had past, he had seen buzzard, honey buzzard, sparrowhawk, goshawk, peregrine, kestrel, hobby and red kite! All these, apart from the red kite, are quite longstanding species found in the New Forest. Goshawks nest regularly in small numbers, buzzards and sparrowhawks are resident all year round and honey buzzards are summer visitors to breed in small numbers. Hobbies - also summer migrants coming here to breed - are a heathland speciality, so the new forest is a good place to see them (and have a chance of doing so); seeing one hawking at speed for flying insects or small birds is a fantastic sight, which I have managed tow or three times in the forest or nearby. At first glance they can look like an overlarge swift.
Red kites were very rare hereabouts twenty years ago, but seeing them everywhere is an increasingly common phenomenon, including drifting over larger urban centres like Salisbury and Winchester. Peregrines seen in the New Forest could be visiting to hunt, from nest sights in urban areas, or be nesting locally.
Finally, at this time of year, if one remembers the most easily overlooked piece of advice for bird-watching - "birds fly, so look upwards!" - it is just possible that you might see an osprey on the closing stages of its spring migration from Africa to the English north and midlands, Wales or Scotland, as it crosses the New Forest or other parts of Hampshire and Wiltshire. Indeed, one was reported about three days ago passing over Mike McMeeken's home town.