Do some research on the Grantown-on-Spey area, Anywhere from the Newtonmore to Carbridge area on Speyside, for Eagles, Cresties and loads more: HERE'S a list of sites in the Cairngorms National Park which you could look at for more information. Loch Garten is the main place to see the Crested Tit in Scotland really.
Also consider the Isle of Mull; no Crested Tits there, but loads of eagles and other Scottish specialities. Here's our Opus article on the Island and if you've not been it's a must : https://www.birdforum.net/opus/Isle_of_Mull
I'm sure others will be along with more information for you too.
I've been twice, once in October (shirt-sleeve weather) and again at Easter (with a group of Birdforum Members). Loads of birds to see there, October, particularly, is noted for the influx of White-fronted Geese.
For Speyside, late winter/early spring is probably best for seeing Crested Tits which are less visible later in spring, but not impossible. For everything else, late spring as there will still be some winter visitors about with some of the earlier summer visitors arriving as well.
Always a difficult question as depends on what you really want to see. Everyone comes spring though that is the hardest time to see Crested Tits for example which are far easier in late autumn winter. Long summer days can make looking for Eagles harder, far easier again in winter with shorter days. Summer plumaged Divers and Slavonian Grebes any time during summer, though be aware there are periods when nesting they become more elusive.
We are trying to discourage ANY searching for Capercaillie now in Spring and summer and encourage birders to only try for this species in Autumn and winter.
Grantown on Spey and surrounding villages are ideal bases with ample accommodation.
I would say that to see Crested Tits you would be in areas that are perhaps not the best areas to have a very good chance of seeing Eagles, there is more chance seeing Eagles to the west of Scotland, especially on the islands. Islay has been mentioned as venue to see Eagles and I have seen Goldens there, I have found Lewis and Harris or Mull or Skye as better destinations to see both Golden and White tailed Eagles. There are Golden and White tailed Eagles in the Highlands/Cairngorms, but they are less often seen, I saw Eagles every day on Lewis, I don't see Eagles every month in the Cairngorms, sadly I think this is linked to disturbance on the shooting estates in the east.