No chance of seeing a crested tit in this area unfortunately, you really would have to go to known hot-spots in the Highlands, and you're looking at a 3-4 hour drive each way from Ayrshire.
There are no known white-tailed eagle nests in the area (at least not known to the general public) but sometimes young birds are spotted in the Clyde area, normally around southern Loch Lomond, but with any large birds of prey, you just have to be lucky to see them, so I would come NOT expecting to see them.
Over on Arran (which you can get to from Ardrossan a little further up the coast) you may have a better chance of seeing golden eagles.
Down the coast from Wemyss Bay is Ballantrae where they have a little tern colony on the shingle beach - you'd need to keep your distance to avoid disturbing them though. While down that way, go into Girvan and you can get a boat trip out to Ailsa Craig where you can see lots of seabirds including puffins, gannets and Manx shearwaters en route.
A bit closer to Wemyss Bay is Ayr. The area around Doonfoot, where the river Doon goes into the sea is good for waders any time of year, and earlier this year I had really good views of common and Sandwich terns, and the harbour area is home to otters (I've seen them twice) and black guillemots.
A bit further inland is the Lochwinnoch RSPB reserve where there are lots of warblers, spotted flycatchers and other woodland birds, and water birds too - most of the common ducks and some of the geese.
I'll let others give you more info about the North Ayrshire coast, including it's best seawatching point - Cloch Point, although it might not be the best time of year for that.
This is a good website for the area:
http://www.ayrshire-birding.org.uk/