As well as all that Wasley's has mentioned about Inverness there is also the very scenic train ride down to Kyle of Lochalsh (which makes a direct connection with the Caledonian Sleeper).
You could even go to Ullapool for the day on the Citylink bus #961 which connects to the Stornoway ferry (or the D and E alternative bus). Anyone can and does use that bus, not just ferry passengers. As well as other things to do in Ullapool there are the wildlife cruises around the Summer Isles- https://www.summerqueen.co.uk/
At Ullapool there is even a connecting bus now to Lochinver- further up the NC500.
A few weeks ago someone posted a newspaper article about the Top 25 places in the world to visit this year. One of those was the Flow Country at Forsinard- that is another possible day trip by train from Inverness. At three hours each way it is a longish but scenic way, but one a lot of Brits at least don't even think twice about.
As you have mentioned it is only two hours from Edinburgh to the Lake District- on what is essentially an hourly service. Lots of people from the Lake District go to Edinburgh or Glasgow on the train for the day. From the Lake District I can get ten hours in either city, and quite often do.
To get a little of the obligatory fix of Edinburgh you could book the 0755 LNER Kings Cross bound train from Inverness (first class is a great bargain usually on that train for your included breakfast, normally only around £15 more than standard). That arrives at Waverley at 1115. You can have the afternoon in Edinburgh then take the 1812 to the Lake District (I normally take the last train two hours later). That gets you into either Windermere or Keswick at just after 2030, or even Pooley Bridge (Ullswater) at just after 2100.
When you get off the Sleeper at Inverness don't forget the Sleeper Lounge just across the street from the station- open for arriving passengers to shower or have breakfast.
Off the 0755 you could stopover in Stirling rather than Edinburgh. If you do that a pro-tip is that it is usually cheaper to buy a Stirling to Penrith/Oxenholme Advance (train specific) Ticket as that basically gives you free travel from Stirling to either Edinburgh or Glasgow to make your connection south.