the first two weeks of June are prime time. especially if there is rain.
if you are in the Perth Area at all, The Newtyle fishings on the Tay are said to be outstanding, and are on my bucket list - i have fished the Tummel above Pitlochry though, nice water. good trout and grayling there too.
further north - i would fish the Spey river, due to its history and scenery - with the peaks of Aviemore in the background its very picturesque.
contrary to popular belief, day tickets are available on most scottish salmon rivers (and Irish ones) as local associations hold fishing rights - in this case the Strath Spey association :
that site shows that day tickets have access to 4 miles of double bank fishing (so 8 miles of water) plus weekly tickets have access to the most famous salmon fishing beat in the world - Upper Castle Grant.
imho the $300 or so weekly ticket is worth it just to fish that 2 mile beat.
i fished it in the 80's with my dad and i still treasure the memories of that day - we had no idea where we were going when we paid ten pounds in the newsagent in Grantown that morning....
that site will also point you to fish pal.
fish pal is the salmon fishers best friend - it lists daily all the salmon beats available in the UK, and you can pay online the night before or same day and go fish.
this is brilliant when the rivers are high or low - there is always somewhere fishable as long as you have a car:
like anywhere in Ireland or Scotland, the locals always know what the fishing is like - ask in the pub, newsagents or ironmongers/hardware store.
if the rivers are in true drought or flood, you can always head to the lochs - lochy, Ness, Broom etc and hire a boatman or fish the inlets outlets etc.
also, ignore the purists - plenty plenty of salmon are caught on big devon minnows spinning each year, so if the small ally's GP's etc are not working, break out the sink tips and large tubes, needles etc - sunray shadows, dee monkeys, scandinavian tube flies etc.
all of which you can fish on a switch rod if you want - though i'd suggest taking a switch and a spey rod too.
all the very best for your trip.