Hi Hamish,
I have fished Mayo on and off for the last 10 Years. As Rattrala says the best pools are the Ridge and the Cathedral.
The Ridge in August is let with five rods on a two session per day basis. It is in the centre of the town, Ballina, with a busy road bridge overlooking it, so if you do not mind the almighty cheer that goes up when you hook a fish, that is the beat for you. The Cathedral is the next beat downstream and has about ten rods but only until 6 pm when it becomes the "Community " beat for the locals, but you can fish it from dawn and the hotel I was staying at would deliver your breakfast to the beat!
The River Moy was massively dredged in the 30' and 40's to improve drainage with the result that it is in many parts very deep and slow moving, with very little fly water. Bait using the "Moy Bung" with worm or prawn is common. At most times, patricularly the less pricey, beats are busy. Most cost no more than 20 to 25 Euros.
The beats I have enjoyed on the fly are parts of Cloongee and Gannons. I was told that the best kept secret are the Upper Waters of the Moy above Foxford. Can't comment because I ain't fished it, but it would be worth a try but as you only have two days, you would probably be better sticking to the lower river.
As for the loughs, they are great, Conn, Cullen, Mask and Corrrib are all within reach. Most of the boat hirers or ghillies will not hire a boat to someone who does not know the water, they really can be treacherous as there are numerous rocks just below the surface, although many are marked. Conn is not so rocky so you can normally hire a boat for the day without too much trouble.
Judd Ruane is a well known character in Ballina having been the proprietor of the Riverboat Inn for many a year. I went out with Judd when he was just starting the sea trout charters, to be recommended.
As you only have two days, planning is all. I had a locally produced fishing magazine which I have not been able to put my hands on, but if I can find it, I will let you have it.
Best regards,
Lyall