In Edinburgh you have Holyrood Distillery and also Port of Leith distillery.
The process of making whisky is similar whichever distillery you visit. The taste of the different whiskies depends upon a variety of factors - the water used, how the malt is dried (peat gives the characteristic smokey taste) the shape of the still, the casks it is matured in and how long it is aged for....
If dependent on public transport, and want to sample a wide range of different whiskies, you might do better by visiting somewhere like the Scottish Whisky Experience in Edinburgh which offers tours testing different single malt whiskies.
Also you will find pubs in Edinburgh with a wide range of whiskies for you to sample. Ideas here.
When you say castles, are you thinking about ruined castles or those that are furnished/still lived in?
Edinburgh and Stirling Castles have already been mentioned as has Holyrood House. This is the only furnished palace I can think of that is open in January. Most don’t open until Easter.
There is the ruined Craigmillar Castle in Edinburgh (accessible by bus).
Linlitgow with its ruined palace is a short train trip from Edinburgh.
Think about a day trip to St Andrews with its ruined castle - train to Leuchars and then bus or taxi to St Andrews. If you catch a bus, get off in Guardbridge for Eden Mill Distillery Which distils gin as well as whisky) and then catch a later bus to St Andrews.